Question:
In triangle ABC with coordinates A=(-7, -10), B=(-2, -3), and C=(-3, -6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 17.10°


Question:
For triangle with vertices A=(-1, -6), B=(4, 1), and C=(-7, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (0.304, -1.217)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, 7), B=(-7, -5), and C=(2, -3). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.176


Question:
Consider triangle ABC with coordinates A=(3, 5), B=(-2, -8), and C=(-1, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.951


Question:
Given triangle ABC with coordinates A=(2, -9), B=(8, 8), and C=(-3, 10), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (4.945, 7.196)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, 3), B=(7, 4), and C=(8, 0). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.721


Question:
In triangle ABC with coordinates A=(0, -6), B=(7, 7), and C=(-1, 6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 54.57°


Question:
Given triangle ABC with coordinates A=(1, 3), B=(-7, 0), and C=(7, 6), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (58.000, -130.000)


Question:
Consider triangle ABC with coordinates A=(-2, 1), B=(10, -3), and C=(5, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.626


Question:
For triangle with vertices A=(6, 7), B=(-5, -3), and C=(-3, 7), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-5.000, 9.200)


Question:
Consider triangle ABC with coordinates A=(-9, 6), B=(5, 1), and C=(3, -9). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.388


Question:
Given a triangle with vertices A=(-4, 4), B=(6, 5), and C=(6, 1), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 84.29°


Question:
Given triangle ABC with coordinates A=(4, 7), B=(-1, 5), and C=(5, 2), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.444, 5.889)


Question:
Given triangle ABC with coordinates A=(-4, -6), B=(-1, -8), and C=(-5, -1), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-11.000, -10.000)


Question:
Given a triangle with vertices A=(-10, 5), B=(10, 6), and C=(-1, 7), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 8.06°


Question:
For triangle with vertices A=(1, 8), B=(9, -10), and C=(-3, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (0.273, 7.455)


Question:
Given a triangle with vertices A=(4, 2), B=(1, -1), and C=(-2, 4), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 75.96°


Question:
Given triangle ABC with coordinates A=(-8, 10), B=(4, -10), and C=(-6, -1), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-31.870, -16.522)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, 8), B=(-6, -2), and C=(-3, 5). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.223


Question:
Consider triangle ABC with coordinates A=(-5, 7), B=(-4, 0), and C=(-1, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.158


Question:
In triangle ABC with coordinates A=(-5, -8), B=(-3, 4), and C=(-1, 1), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 43.15°


Question:
Consider triangle ABC with coordinates A=(4, -1), B=(-2, 5), and C=(-8, 2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.959


Question:
Consider triangle ABC with coordinates A=(-7, 10), B=(9, 2), and C=(7, -10). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.819


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, -1), B=(6, -3), and C=(4, 4). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.080


Question:
Given triangle ABC with coordinates A=(-1, 3), B=(-3, 4), and C=(-1, -2), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (2.000, 4.000)


Question:
For triangle with vertices A=(-7, 3), B=(4, 3), and C=(-2, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-2.000, 8.000)


Question:
Given a triangle with vertices A=(4, 6), B=(-7, 9), and C=(8, -3), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 23.40°


Question:
Given a triangle with vertices A=(-9, -7), B=(-5, -8), and C=(9, 1), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 133.23°


Question:
Given triangle ABC with coordinates A=(-1, 4), B=(4, -6), and C=(0, -7), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (1.556, -6.222)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, 9), B=(-10, -2), and C=(-6, -4). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.828


Question:
For triangle with vertices A=(9, -5), B=(1, 7), and C=(9, 1), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (18.000, 7.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-7, 6), B=(5, 8), and C=(-5, 4). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.087


Question:
In triangle ABC with coordinates A=(6, -7), B=(0, -7), and C=(-1, -5), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 116.57°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, 3), B=(4, -9), and C=(6, 5). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.080


Question:
Consider triangle ABC with coordinates A=(4, 2), B=(-4, -1), and C=(-9, 3). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.679


Question:
Find the incircle radius of triangle ABC whose vertices are A=(0, -4), B=(-3, -4), and C=(-7, -1). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.576


Question:
Given triangle ABC with coordinates A=(-7, -1), B=(-2, 3), and C=(-9, 10), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-3.222, 2.778)


Question:
For triangle with vertices A=(4, 1), B=(9, -5), and C=(-3, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (4.355, 3.129)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(2, 7), B=(3, 1), and C=(1, 7). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.448


Question:
In triangle ABC with coordinates A=(4, 0), B=(7, 7), and C=(2, 5), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 45.00°


Question:
Given triangle ABC with coordinates A=(5, 6), B=(-1, -5), and C=(-5, -2), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-2.161, -3.548)


Question:
Consider triangle ABC with coordinates A=(4, -8), B=(-6, 2), and C=(-9, -9). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.629


Question:
In triangle ABC with coordinates A=(-1, -9), B=(5, -10), and C=(6, 0), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 86.25°


Question:
For triangle with vertices A=(9, -7), B=(0, -4), and C=(-3, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-8.905, -13.714)


Question:
For triangle with vertices A=(7, 0), B=(-10, -8), and C=(6, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (13.371, -5.663)


Question:
For triangle with vertices A=(-4, 7), B=(-7, -2), and C=(0, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-21.333, 17.111)


Question:
Consider triangle ABC with coordinates A=(-4, 0), B=(-5, 10), and C=(-10, 6). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.165


Question:
For triangle with vertices A=(9, -2), B=(-6, 1), and C=(-8, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-6.324, 2.378)


Question:
For triangle with vertices A=(-8, 5), B=(8, 8), and C=(-1, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-3.695, 24.373)


Question:
For triangle with vertices A=(8, -5), B=(-5, 2), and C=(4, 4), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (5.416, 6.629)


Question:
Consider triangle ABC with coordinates A=(6, 8), B=(7, 7), and C=(8, -2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.387


Question:
Consider triangle ABC with coordinates A=(8, 1), B=(-7, -8), and C=(1, -6). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.178


Question:
Given a triangle with vertices A=(-5, -7), B=(-2, -1), and C=(3, -10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 55.62°


Question:
In triangle ABC with coordinates A=(6, 7), B=(-6, 5), and C=(-10, -6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 119.45°


Question:
Consider triangle ABC with coordinates A=(0, 2), B=(-4, -7), and C=(0, -9). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.738


Question:
Given triangle ABC with coordinates A=(3, 1), B=(-9, 8), and C=(-10, 7), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-7.421, 11.421)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, -9), B=(1, 3), and C=(-9, 5). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.299


Question:
Consider triangle ABC with coordinates A=(2, -4), B=(9, -5), and C=(-3, -3). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.082


Question:
Given triangle ABC with coordinates A=(4, 4), B=(-5, 2), and C=(1, 3), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (13.667, -54.000)


Question:
In triangle ABC with coordinates A=(-4, 7), B=(1, 4), and C=(-9, 6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 19.65°


Question:
For triangle with vertices A=(9, 1), B=(-5, 7), and C=(9, -5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (14.143, 7.000)


Question:
Given a triangle with vertices A=(4, -4), B=(-8, 9), and C=(-7, 10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 92.29°


Question:
For triangle with vertices A=(-10, -5), B=(-7, -6), and C=(-7, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-6.000, -5.000)


Question:
Given a triangle with vertices A=(1, 8), B=(-7, -10), and C=(-1, 6), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.41°


Question:
Given a triangle with vertices A=(5, -10), B=(7, 6), and C=(5, -9), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.47°


Question:
For triangle with vertices A=(9, 8), B=(3, 5), and C=(-1, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-11.778, 15.556)


Question:
For triangle with vertices A=(-8, 2), B=(-2, 2), and C=(-4, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-4.000, 1.200)


Question:
Consider triangle ABC with coordinates A=(-3, 4), B=(4, 7), and C=(-9, -7). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.503


Question:
Consider triangle ABC with coordinates A=(9, -3), B=(3, 5), and C=(-2, 10). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.293


Question:
Given triangle ABC with coordinates A=(0, 5), B=(-4, 2), and C=(3, 9), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (24.000, -19.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, 9), B=(-1, 4), and C=(3, -5). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.885


Question:
Given triangle ABC with coordinates A=(10, -2), B=(-10, 5), and C=(7, 1), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (18.308, 33.308)


Question:
Given triangle ABC with coordinates A=(8, -7), B=(0, -3), and C=(10, 9), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.765, -3.471)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-4, -7), B=(7, -7), and C=(0, 7). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.737


Question:
In triangle ABC with coordinates A=(9, 7), B=(-1, -10), and C=(10, -7), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 44.28°


Question:
For triangle with vertices A=(-5, -5), B=(-4, 2), and C=(-5, 7), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (30.000, 2.000)


Question:
In triangle ABC with coordinates A=(10, -5), B=(-1, -7), and C=(1, -1), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 61.26°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-5, 7), B=(7, 3), and C=(-7, -8). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 4.124


Question:
Given a triangle with vertices A=(-3, -4), B=(10, 8), and C=(4, -8), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 26.73°


Question:
Given triangle ABC with coordinates A=(-4, 8), B=(2, 10), and C=(-5, 9), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-3.500, 4.500)


Question:
Given a triangle with vertices A=(-4, 9), B=(-1, -8), and C=(1, -3), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 31.81°


Question:
For triangle with vertices A=(-2, -8), B=(3, -2), and C=(-7, -9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (6.680, -20.400)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, -10), B=(-5, -9), and C=(3, -2). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.910


Question:
Given triangle ABC with coordinates A=(-3, 9), B=(-1, 8), and C=(-5, 1), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-1.444, 8.111)


Question:
In triangle ABC with coordinates A=(-9, 8), B=(9, 4), and C=(-3, 10), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 14.04°


Question:
For triangle with vertices A=(9, 8), B=(8, -7), and C=(-10, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (12.247, -11.483)


Question:
Given triangle ABC with coordinates A=(2, 6), B=(1, -6), and C=(5, -10), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-12.538, -8.538)


Question:
Given a triangle with vertices A=(6, -2), B=(-9, 2), and C=(10, -3), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.19°


Question:
Given a triangle with vertices A=(3, -2), B=(4, 10), and C=(4, -10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 4.76°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(1, 6), B=(-8, 2), and C=(-1, -10). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.411


Question:
Consider triangle ABC with coordinates A=(-6, 3), B=(-9, -5), and C=(-9, -1). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.684


Question:
Consider triangle ABC with coordinates A=(1, 5), B=(0, 9), and C=(0, 7). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.239


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, -4), B=(7, 10), and C=(-6, -10). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.158


Question:
Given a triangle with vertices A=(1, 10), B=(10, 8), and C=(-2, 5), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 26.57°


Question:
Given a triangle with vertices A=(3, 6), B=(-9, 3), and C=(5, -4), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 40.60°


Question:
For triangle with vertices A=(-5, 3), B=(0, -4), and C=(-3, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-6.500, 2.500)


Question:
Given triangle ABC with coordinates A=(2, 4), B=(-1, -4), and C=(6, -2), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.440, -1.040)


Question:
For triangle with vertices A=(9, 7), B=(9, -1), and C=(7, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (85.500, -10.000)


Question:
Given triangle ABC with coordinates A=(-10, -2), B=(-10, 7), and C=(-9, -3), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-20.000, -3.000)


Question:
In triangle ABC with coordinates A=(-10, 8), B=(5, -5), and C=(8, 4), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 67.52°


Question:
Given a triangle with vertices A=(10, 5), B=(-5, 5), and C=(-1, 1), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 45.00°


Question:
For triangle with vertices A=(-9, -10), B=(-3, -6), and C=(-3, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-1.667, -10.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-9, 4), B=(-8, -5), and C=(2, -8). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.432


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, -10), B=(4, -10), and C=(0, 10). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.924


Question:
For triangle with vertices A=(-6, 9), B=(0, -8), and C=(-5, 8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (27.455, 19.455)


Question:
In triangle ABC with coordinates A=(10, -6), B=(2, 4), and C=(9, 4), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 51.34°


Question:
Consider triangle ABC with coordinates A=(10, -9), B=(2, 1), and C=(-1, -2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.795


Question:
Given triangle ABC with coordinates A=(-7, -2), B=(2, -6), and C=(-6, -9), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-5.119, -7.017)


Question:
Consider triangle ABC with coordinates A=(2, -4), B=(-3, -1), and C=(5, -6). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.053


Question:
In triangle ABC with coordinates A=(3, 10), B=(-4, 1), and C=(-1, 1), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 52.13°


Question:
Consider triangle ABC with coordinates A=(10, -6), B=(2, -4), and C=(-8, 9). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.747


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, -9), B=(-2, 3), and C=(8, 8). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.877


Question:
For triangle with vertices A=(2, 5), B=(-4, 4), and C=(6, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.340, 5.957)


Question:
Given a triangle with vertices A=(6, 7), B=(-1, 3), and C=(7, 7), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.18°


Question:
Consider triangle ABC with coordinates A=(3, -3), B=(1, -6), and C=(-3, -5). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.996


Question:
Given a triangle with vertices A=(5, -3), B=(-5, -10), and C=(-10, 1), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 79.45°


Question:
Given a triangle with vertices A=(-3, -7), B=(-9, 3), and C=(8, 0), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 49.03°


Question:
Consider triangle ABC with coordinates A=(-5, 4), B=(-3, 6), and C=(-4, 9). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.721


Question:
For triangle with vertices A=(6, 0), B=(2, -5), and C=(8, 1), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-7.000, 13.000)


Question:
Given a triangle with vertices A=(-4, 7), B=(-5, -3), and C=(10, 8), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 48.04°


Question:
For triangle with vertices A=(10, -4), B=(6, -4), and C=(3, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.000, -6.333)


Question:
In triangle ABC with coordinates A=(9, 4), B=(8, -5), and C=(5, -1), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 43.21°


Question:
Given triangle ABC with coordinates A=(-1, -2), B=(4, 5), and C=(9, 2), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.680, 5.800)


Question:
For triangle with vertices A=(-9, 3), B=(-8, 5), and C=(-3, -5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-14.000, 0.500)


Question:
Given triangle ABC with coordinates A=(10, 9), B=(3, 3), and C=(-10, 0), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (20.211, -35.246)


Question:
Given triangle ABC with coordinates A=(-8, 0), B=(3, 0), and C=(-8, 6), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-8.000, 0.000)


Question:
In triangle ABC with coordinates A=(-7, 6), B=(1, 2), and C=(-5, -3), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 66.37°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, 9), B=(-5, 7), and C=(6, -7). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.912


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, 0), B=(0, -8), and C=(-3, 0). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.852


Question:
Given a triangle with vertices A=(2, 3), B=(-7, 8), and C=(4, -5), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 20.71°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-4, -4), B=(-1, 1), and C=(-9, 2). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.981


Question:
Consider triangle ABC with coordinates A=(5, 6), B=(9, 1), and C=(-3, 3). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.918


Question:
Given triangle ABC with coordinates A=(4, -10), B=(5, 1), and C=(-8, -3), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (2.129, -3.921)


Question:
Consider triangle ABC with coordinates A=(-3, -9), B=(8, 6), and C=(-4, -2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.295


Question:
For triangle with vertices A=(-9, -3), B=(-7, 2), and C=(10, 0), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-7.809, 7.124)


Question:
For triangle with vertices A=(5, 3), B=(8, -4), and C=(2, -9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (11.579, -4.895)


Question:
For triangle with vertices A=(7, 4), B=(10, -3), and C=(0, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (11.870, 10.087)


Question:
Given triangle ABC with coordinates A=(-7, -8), B=(-9, 6), and C=(-1, 4), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-4.111, 3.556)


Question:
For triangle with vertices A=(-8, -10), B=(9, -2), and C=(-7, 8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-2.597, -1.356)


Question:
Given a triangle with vertices A=(-7, -9), B=(0, 0), and C=(-4, -1), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 38.09°


Question:
Consider triangle ABC with coordinates A=(1, -3), B=(-3, 0), and C=(1, -1). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.719


Question:
Given triangle ABC with coordinates A=(-8, -10), B=(1, -1), and C=(-3, -8), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (8.333, -19.333)


Question:
Consider triangle ABC with coordinates A=(-10, -3), B=(0, 0), and C=(0, 9). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.567


Question:
For triangle with vertices A=(-6, -6), B=(-1, 8), and C=(5, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (0.333, 6.667)


Question:
Consider triangle ABC with coordinates A=(3, 7), B=(4, -7), and C=(5, -7). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.480


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, -3), B=(5, 4), and C=(-5, 8). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.806


Question:
Given a triangle with vertices A=(-3, -2), B=(-10, -3), and C=(-8, -2), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 18.43°


Question:
Consider triangle ABC with coordinates A=(-2, -6), B=(8, 7), and C=(-7, 2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.482


Question:
For triangle with vertices A=(-5, 0), B=(1, -4), and C=(-3, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-6.895, -0.842)


Question:
Given a triangle with vertices A=(7, 6), B=(6, -6), and C=(2, 10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 18.80°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, -8), B=(4, -1), and C=(3, 0). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.633


Question:
In triangle ABC with coordinates A=(4, -5), B=(-1, 7), and C=(-2, 6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 67.62°


Question:
Given a triangle with vertices A=(-8, 8), B=(-6, 1), and C=(2, -2), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 126.50°


Question:
In triangle ABC with coordinates A=(2, -9), B=(10, -4), and C=(-4, 2), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 55.20°


Question:
Given a triangle with vertices A=(6, 10), B=(-10, -4), and C=(3, 10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 5.94°


Question:
In triangle ABC with coordinates A=(-10, -6), B=(-5, -10), and C=(-4, 8), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 54.52°


Question:
For triangle with vertices A=(8, 5), B=(-7, 5), and C=(4, -9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (4.000, 1.857)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(1, -2), B=(-3, 8), and C=(0, 7). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.131


Question:
For triangle with vertices A=(-4, -10), B=(-6, 9), and C=(-2, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-6.000, -10.421)


Question:
For triangle with vertices A=(0, 3), B=(-10, -1), and C=(0, 5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (2.400, -1.000)


Question:
Consider triangle ABC with coordinates A=(10, 5), B=(3, -4), and C=(-4, 2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.005


Question:
For triangle with vertices A=(-9, 5), B=(9, -4), and C=(-10, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-20.143, -11.286)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, 8), B=(-4, -6), and C=(3, 5). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.641


Question:
Consider triangle ABC with coordinates A=(5, -7), B=(7, 5), and C=(4, -3). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.805


Question:
Given triangle ABC with coordinates A=(-8, -1), B=(-3, -6), and C=(-3, -3), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-1.000, -1.000)


Question:
Given a triangle with vertices A=(9, -3), B=(-5, -10), and C=(1, -6), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 7.13°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, -4), B=(-9, 8), and C=(8, -2). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.293


Question:
In triangle ABC with coordinates A=(-10, -5), B=(8, -1), and C=(-8, 10), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 47.04°


Question:
Consider triangle ABC with coordinates A=(-10, 2), B=(-5, -10), and C=(10, -1). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 4.436


Question:
Given a triangle with vertices A=(1, -3), B=(-10, 0), and C=(10, 7), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 34.55°


Question:
Consider triangle ABC with coordinates A=(9, -9), B=(8, -9), and C=(-1, 7). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.419


Question:
For triangle with vertices A=(3, -3), B=(-1, -10), and C=(-4, 3), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (5.493, -2.425)


Question:
In triangle ABC with coordinates A=(1, 3), B=(-1, 10), and C=(7, 4), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 37.18°


Question:
Given triangle ABC with coordinates A=(10, 0), B=(-7, -1), and C=(-3, -8), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-3.033, -7.447)


Question:
Given triangle ABC with coordinates A=(10, -5), B=(5, 5), and C=(-10, 2), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (6.909, 10.455)


Question:
Consider triangle ABC with coordinates A=(-3, -5), B=(-2, -3), and C=(-7, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.898


Question:
Consider triangle ABC with coordinates A=(-5, -7), B=(9, 1), and C=(0, -4). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.062


Question:
Given a triangle with vertices A=(10, 0), B=(6, -9), and C=(0, -7), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 95.53°


Question:
Given a triangle with vertices A=(-3, -3), B=(4, -2), and C=(2, 3), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 76.33°


Question:
For triangle with vertices A=(3, -8), B=(5, -2), and C=(7, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (5.714, -2.571)


Question:
Given triangle ABC with coordinates A=(-3, -1), B=(-1, -9), and C=(-10, 5), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (16.727, 11.682)


Question:
Consider triangle ABC with coordinates A=(1, 4), B=(-4, 2), and C=(7, 10). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.655


Question:
For triangle with vertices A=(-4, 4), B=(-8, 7), and C=(-3, -7), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (8.634, 8.512)


Question:
In triangle ABC with coordinates A=(-3, -5), B=(9, -6), and C=(-4, 1), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 23.54°


Question:
Consider triangle ABC with coordinates A=(-9, 10), B=(7, 8), and C=(9, -9). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 4.511


Question:
Consider triangle ABC with coordinates A=(1, -8), B=(4, -3), and C=(3, 3). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.996


Question:
Given a triangle with vertices A=(-3, 8), B=(-3, -3), and C=(4, 8), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 32.47°


Question:
In triangle ABC with coordinates A=(-6, -3), B=(7, 3), and C=(-2, 10), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 62.65°


Question:
Given a triangle with vertices A=(-5, -1), B=(7, -10), and C=(3, -10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 36.87°


Question:
For triangle with vertices A=(-6, 2), B=(0, 8), and C=(-3, -4), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-10.000, 3.000)


Question:
Consider triangle ABC with coordinates A=(-7, -3), B=(-8, -8), and C=(-2, -2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.285


Question:
In triangle ABC with coordinates A=(10, -5), B=(6, -3), and C=(5, 7), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 122.28°


Question:
Consider triangle ABC with coordinates A=(-2, -9), B=(8, 3), and C=(6, 5). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.273


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, -9), B=(-3, -8), and C=(-8, -10). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.808


Question:
Given a triangle with vertices A=(1, 5), B=(1, -8), and C=(2, -6), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 26.57°


Question:
Given a triangle with vertices A=(5, -5), B=(-3, 3), and C=(-9, -5), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 81.87°


Question:
Consider triangle ABC with coordinates A=(-8, 3), B=(10, -8), and C=(-8, -6). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.361


Question:
For triangle with vertices A=(-4, -6), B=(3, -7), and C=(3, -9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.429, -6.000)


Question:
Given a triangle with vertices A=(-9, -9), B=(0, -6), and C=(9, 6), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 145.30°


Question:
In triangle ABC with coordinates A=(7, -7), B=(1, -8), and C=(-3, 9), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 93.78°


Question:
Consider triangle ABC with coordinates A=(-10, 5), B=(6, 9), and C=(5, 6). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.268


Question:
In triangle ABC with coordinates A=(0, 3), B=(-9, 4), and C=(8, -1), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 10.05°


Question:
In triangle ABC with coordinates A=(3, 2), B=(8, 4), and C=(-8, 1), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 11.18°


Question:
For triangle with vertices A=(-1, 5), B=(-8, 4), and C=(0, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (1.037, 1.741)


Question:
Given triangle ABC with coordinates A=(6, 2), B=(1, -8), and C=(4, -5), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (22.000, -14.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(0, -10), B=(1, 5), and C=(-9, 9). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.289


Question:
Find the incircle radius of triangle ABC whose vertices are A=(5, -4), B=(4, -7), and C=(0, -2). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.137


Question:
Find the incircle radius of triangle ABC whose vertices are A=(10, 10), B=(5, 7), and C=(-5, -10). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.088


Question:
Consider triangle ABC with coordinates A=(2, -5), B=(7, -8), and C=(-9, 7). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.613


Question:
Find the incircle radius of triangle ABC whose vertices are A=(2, 8), B=(8, 4), and C=(-3, 3). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.974


Question:
Given a triangle with vertices A=(-10, -1), B=(7, -6), and C=(-4, 0), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 12.22°


Question:
In triangle ABC with coordinates A=(7, 2), B=(3, -6), and C=(10, 10), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.94°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, -2), B=(3, 0), and C=(-4, -10). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.537


Question:
Given triangle ABC with coordinates A=(0, 10), B=(10, 8), and C=(-9, 1), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-4.667, 22.667)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, 3), B=(1, 2), and C=(-9, 4). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.293


Question:
Consider triangle ABC with coordinates A=(3, -7), B=(-2, 7), and C=(7, 6). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.225


Question:
In triangle ABC with coordinates A=(-8, -6), B=(7, 3), and C=(-4, -6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 8.33°


Question:
Given triangle ABC with coordinates A=(7, -8), B=(3, 9), and C=(5, 10), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-1.263, 8.526)


Question:
Given triangle ABC with coordinates A=(-8, 3), B=(8, 8), and C=(5, -4), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (3.729, 0.068)


Question:
Consider triangle ABC with coordinates A=(-10, -5), B=(-9, 7), and C=(8, -2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 4.301


Question:
Consider triangle ABC with coordinates A=(7, 3), B=(4, 0), and C=(1, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.645


Question:
Given a triangle with vertices A=(3, 0), B=(9, 2), and C=(-2, -6), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 17.59°


Question:
In triangle ABC with coordinates A=(-1, 7), B=(-4, 6), and C=(-5, 0), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 117.90°


Question:
Consider triangle ABC with coordinates A=(5, 0), B=(5, 6), and C=(0, -4). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.272


Question:
For triangle with vertices A=(7, -7), B=(4, -4), and C=(7, 2), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (1.000, -4.000)


Question:
For triangle with vertices A=(-10, 4), B=(0, -7), and C=(-10, 7), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-25.400, -7.000)


Question:
Given a triangle with vertices A=(7, 0), B=(-9, 3), and C=(-7, -5), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 65.34°


Question:
For triangle with vertices A=(-10, -8), B=(9, -1), and C=(-4, 0), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-8.455, 12.091)


Question:
Given triangle ABC with coordinates A=(1, -8), B=(9, -1), and C=(-10, 8), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (2.054, -5.776)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(10, 1), B=(0, -5), and C=(1, 6). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.151


Question:
Find the incircle radius of triangle ABC whose vertices are A=(1, -8), B=(10, 5), and C=(0, 1). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.638


Question:
For triangle with vertices A=(10, 8), B=(-3, -1), and C=(9, 8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-3.000, 25.333)


Question:
For triangle with vertices A=(4, 1), B=(3, -9), and C=(-4, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (5.710, -10.971)


Question:
For triangle with vertices A=(8, 1), B=(7, -1), and C=(0, -5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (16.000, -13.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, -4), B=(0, -2), and C=(-2, -10). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.402


Question:
Given triangle ABC with coordinates A=(-5, -4), B=(-9, -5), and C=(5, 8), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (12.789, -23.158)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(5, -2), B=(-9, 5), and C=(10, 5). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.075


Question:
Consider triangle ABC with coordinates A=(1, -9), B=(5, -5), and C=(-5, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.170


Question:
Find the incircle radius of triangle ABC whose vertices are A=(4, 10), B=(-8, 10), and C=(-2, 4). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.485


Question:
Given triangle ABC with coordinates A=(-1, -2), B=(-7, 4), and C=(4, 6), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-1.462, 0.538)


Question:
In triangle ABC with coordinates A=(-9, 5), B=(2, 0), and C=(-6, -7), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 65.63°


Question:
Given a triangle with vertices A=(-10, -6), B=(6, -2), and C=(4, 10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 94.57°


Question:
Given triangle ABC with coordinates A=(-2, 1), B=(-7, 4), and C=(-1, 6), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-2.714, 3.143)


Question:
Given a triangle with vertices A=(-1, 2), B=(8, 8), and C=(4, -8), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 42.27°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, 0), B=(-8, -8), and C=(3, 3). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.517


Question:
In triangle ABC with coordinates A=(-10, 0), B=(-2, -7), and C=(-5, 3), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 32.11°


Question:
Consider triangle ABC with coordinates A=(5, 5), B=(5, -9), and C=(6, 3). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 0.495


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-5, -8), B=(4, -10), and C=(-10, 2). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.060


Question:
In triangle ABC with coordinates A=(0, 5), B=(8, -10), and C=(-6, -3), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 35.36°


Question:
Given a triangle with vertices A=(5, 10), B=(6, -8), and C=(2, 10), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 9.35°


Question:
For triangle with vertices A=(-1, -6), B=(0, -4), and C=(7, 8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-217.000, 120.000)


Question:
Consider triangle ABC with coordinates A=(5, -7), B=(-3, 6), and C=(6, 3). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.672


Question:
For triangle with vertices A=(-9, 5), B=(-4, -8), and C=(3, 9), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-8.227, 4.682)


Question:
Consider triangle ABC with coordinates A=(5, 0), B=(8, 5), and C=(-8, -2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.619


Question:
For triangle with vertices A=(-2, 1), B=(6, -9), and C=(10, 8), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (0.511, 0.409)


Question:
In triangle ABC with coordinates A=(1, 2), B=(-9, 0), and C=(-7, -7), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 85.36°


Question:
For triangle with vertices A=(7, 10), B=(6, -5), and C=(9, -5), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (7.000, -4.867)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, -4), B=(-10, 4), and C=(6, 8). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 4.136


Question:
Given a triangle with vertices A=(1, 1), B=(-10, 5), and C=(1, 6), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 25.18°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(10, 5), B=(7, 4), and C=(10, -3). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.278


Question:
Given a triangle with vertices A=(7, 7), B=(3, 5), and C=(-4, -9), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 143.13°


Question:
For triangle with vertices A=(-3, -4), B=(-8, 8), and C=(9, -2), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-5.338, -7.974)


Question:
For triangle with vertices A=(-4, 3), B=(6, 4), and C=(-9, -3), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-11.127, 18.273)


Question:
Given triangle ABC with coordinates A=(8, 8), B=(2, 10), and C=(-1, 6), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (1.333, 13.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, -4), B=(-2, 9), and C=(-4, 3). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.190


Question:
Given a triangle with vertices A=(6, -1), B=(-1, 6), and C=(5, 3), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 18.43°


Question:
Given triangle ABC with coordinates A=(-6, 2), B=(1, 1), and C=(6, -2), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (10.500, 29.500)


Question:
Given triangle ABC with coordinates A=(-1, -10), B=(-6, -4), and C=(-3, -4), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-1.000, -2.333)


Question:
Given a triangle with vertices A=(-8, -4), B=(-2, -5), and C=(-1, 8), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 84.94°


Question:
Consider triangle ABC with coordinates A=(-2, -8), B=(3, 5), and C=(-6, -2). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.520


Question:
In triangle ABC with coordinates A=(-6, 2), B=(-9, -6), and C=(0, -3), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 51.01°


Question:
In triangle ABC with coordinates A=(-5, 3), B=(5, -10), and C=(-4, -6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 28.47°


Question:
For triangle with vertices A=(4, -7), B=(-5, -10), and C=(10, 10), determine the orthocenter (intersection of altitudes). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (19.556, -18.667)


Question:
Consider triangle ABC with coordinates A=(3, 0), B=(-10, 1), and C=(8, 10). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.044


Question:
Given triangle ABC with coordinates A=(-10, 0), B=(-10, -3), and C=(-3, 5), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-15.714, 5.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-10, 2), B=(-10, -4), and C=(-3, 7). For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.519


Question:
Given a triangle with vertices A=(10, -9), B=(4, 2), and C=(3, -5), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 36.74°


Question:
Given triangle ABC with coordinates A=(-9, 7), B=(9, 9), and C=(2, 9), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (-9.000, 108.000)


Question:
Consider triangle ABC with coordinates A=(6, 10), B=(-8, 4), and C=(7, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.578


Question:
Consider triangle ABC with coordinates A=(2, -6), B=(1, 7), and C=(4, 0). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 1.186


Question:
In triangle ABC with coordinates A=(3, -6), B=(-8, -3), and C=(-1, 0), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 38.45°