Question:
Given a triangle with vertices A=(-7, -6), B=(9, -1), and C=(-9, 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: 41.32°


Question:
In triangle ABC with coordinates A=(-5, 5), B=(-8, 7), and C=(3, 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: 1.22°


Question:
In triangle ABC with coordinates A=(-6, 8), B=(-7, -8), 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: 8.95°


Question:
Given triangle ABC with coordinates A=(5, -1), B=(-9, 4), and C=(2, -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: (4.257, -1.681)


Question:
For triangle with vertices A=(6, 4), B=(0, -6), and C=(-6, -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: (1.778, -8.667)


Question:
Given a triangle with vertices A=(6, 0), B=(4, 5), and C=(-8, 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: 111.80°


Question:
Consider triangle ABC with coordinates A=(-1, 6), B=(0, -3), 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: 0.958


Question:
Given a triangle with vertices A=(-8, -9), B=(2, 7), and C=(-10, 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: 27.74°


Question:
Given a triangle with vertices A=(0, -5), B=(-3, 10), 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: 101.31°


Question:
Given triangle ABC with coordinates A=(6, 6), B=(8, 3), and C=(8, 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: (14.000, 6.000)


Question:
Given a triangle with vertices A=(1, 1), B=(-4, 2), and C=(-8, -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: 131.82°


Question:
For triangle with vertices A=(7, 2), B=(3, -6), and C=(1, 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: (1.909, 0.545)


Question:
Given triangle ABC with coordinates A=(-10, 4), B=(7, 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: (-9.252, 5.709)


Question:
For triangle with vertices A=(7, -4), B=(-6, 7), and C=(1, -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: (-3.177, -9.937)


Question:
For triangle with vertices A=(5, 6), B=(1, -10), and C=(6, 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: (1.000, 7.250)


Question:
Given triangle ABC with coordinates A=(3, -2), B=(4, 5), and C=(-4, 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: (7.667, 7.333)


Question:
Given triangle ABC with coordinates A=(10, -6), B=(4, -9), and C=(6, 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: (14.222, -6.444)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, -7), B=(6, 7), 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: 3.719


Question:
Given a triangle with vertices A=(-1, 8), B=(-6, -9), and C=(-9, 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: 27.01°


Question:
Given triangle ABC with coordinates A=(-4, 8), B=(-8, -8), and C=(-8, 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: (-20.000, 8.000)


Question:
For triangle with vertices A=(5, -5), B=(4, 8), 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: (3.025, 6.848)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(2, -7), B=(-1, 6), and C=(9, 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: 3.209


Question:
Consider triangle ABC with coordinates A=(-10, -5), B=(3, -7), and C=(-4, 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: 2.789


Question:
Given a triangle with vertices A=(-4, 9), B=(6, -7), and C=(7, 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: 40.14°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 5), B=(-2, 5), 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: 2.550


Question:
Consider triangle ABC with coordinates A=(-5, -4), B=(-3, 4), and C=(1, -8). 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: 1.992


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, 3), B=(-1, 2), 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: 1.659


Question:
Consider triangle ABC with coordinates A=(-5, 2), B=(0, 10), 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: 2.370


Question:
Given a triangle with vertices A=(8, 1), B=(0, -2), and C=(0, -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: 69.44°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-6, -8), B=(-2, -6), and C=(8, -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: 0.411


Question:
Given triangle ABC with coordinates A=(-8, 2), B=(-8, 9), 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: (-8.000, 2.000)


Question:
Given triangle ABC with coordinates A=(-4, -8), B=(-7, 10), and C=(-6, -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: (10.286, -7.286)


Question:
Given triangle ABC with coordinates A=(-7, 9), B=(2, 0), and C=(-9, -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: (-2.412, 0.588)


Question:
Given a triangle with vertices A=(-9, 5), B=(-2, 3), and C=(3, 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: 113.86°


Question:
Given triangle ABC with coordinates A=(1, -8), B=(-5, -3), and C=(-2, -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: (-27.000, -36.000)


Question:
Given triangle ABC with coordinates A=(-4, 2), B=(-1, -4), 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: (-2.286, -3.143)


Question:
For triangle with vertices A=(6, 2), B=(8, 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: (3.500, 2.000)


Question:
Given triangle ABC with coordinates A=(-1, -3), B=(-8, -4), and C=(-6, 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: (-4.667, -2.333)


Question:
In triangle ABC with coordinates A=(-6, 2), B=(2, 4), and C=(-10, 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: 9.27°


Question:
Given a triangle with vertices A=(6, 9), B=(1, -3), and C=(6, 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: 1.58°


Question:
For triangle with vertices A=(-9, 7), B=(-5, -1), and C=(-8, -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: (7.692, -0.154)


Question:
Given triangle ABC with coordinates A=(-8, 5), B=(-10, -10), and C=(-5, 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: (4.545, -1.273)


Question:
Given a triangle with vertices A=(-1, -6), B=(-1, 9), and C=(-4, 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: 45.00°


Question:
For triangle with vertices A=(5, -7), B=(-6, 6), and C=(2, 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: (15.000, 13.000)


Question:
For triangle with vertices A=(6, 5), B=(-10, 1), and C=(-3, -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: (-5.000, -2.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, -9), B=(-9, -4), and C=(-7, 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: 3.435


Question:
Consider triangle ABC with coordinates A=(-1, -3), B=(9, -9), and C=(-10, 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: 0.133


Question:
For triangle with vertices A=(10, -1), B=(8, 6), and C=(-2, -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: (13.571, -3.551)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 3), B=(3, 9), and C=(-7, -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: 3.204


Question:
For triangle with vertices A=(1, -3), B=(-8, 6), 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: (13.000, 21.000)


Question:
For triangle with vertices A=(-7, -7), B=(-4, -3), and C=(9, 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: (-91.000, 84.000)


Question:
Consider triangle ABC with coordinates A=(-6, 6), B=(-6, -6), and C=(6, 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: 3.450


Question:
For triangle with vertices A=(1, -3), B=(3, -5), and C=(-2, -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: (1.000, -2.000)


Question:
Given a triangle with vertices A=(2, 5), B=(-1, -5), and C=(6, -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: 89.25°


Question:
Given triangle ABC with coordinates A=(6, -7), B=(-3, -8), 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: (-7.839, -14.452)


Question:
Given triangle ABC with coordinates A=(-1, 2), B=(4, -6), and C=(4, 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: (2.400, 2.000)


Question:
For triangle with vertices A=(-4, 7), B=(6, 0), and C=(8, 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: (-4.000, -17.143)


Question:
Given triangle ABC with coordinates A=(0, 8), B=(3, 7), and C=(4, -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: (7.931, 8.793)


Question:
Consider triangle ABC with coordinates A=(5, 8), B=(-10, -4), and C=(-7, -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: 0.234


Question:
For triangle with vertices A=(-2, -6), B=(0, -3), and C=(6, -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: (-0.600, -4.600)


Question:
Given a triangle with vertices A=(6, 2), B=(-6, -3), and C=(5, -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: 42.60°


Question:
In triangle ABC with coordinates A=(2, -9), B=(7, -10), and C=(10, 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: 93.95°


Question:
Given triangle ABC with coordinates A=(5, 2), B=(6, -1), 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: (6.000, 7.333)


Question:
In triangle ABC with coordinates A=(-1, 2), B=(7, 4), 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: 58.86°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-4, -9), B=(-5, -4), and C=(-4, 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: 0.495


Question:
Consider triangle ABC with coordinates A=(1, 1), B=(-5, -8), 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: 1.953


Question:
In triangle ABC with coordinates A=(10, 1), B=(8, 3), and C=(7, -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: 54.46°


Question:
Given a triangle with vertices A=(8, -8), B=(6, 7), 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: 63.97°


Question:
Consider triangle ABC with coordinates A=(-5, 10), B=(-3, -6), and C=(-5, 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: 0.310


Question:
Given a triangle with vertices A=(4, 4), B=(9, -4), 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: 57.99°


Question:
Consider triangle ABC with coordinates A=(0, -5), B=(-10, 3), and C=(4, 8). 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: 3.925


Question:
For triangle with vertices A=(-3, 1), B=(-4, 5), and C=(-8, 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: (-3.238, 1.190)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(0, -10), B=(-6, 9), and C=(9, -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: 3.681


Question:
For triangle with vertices A=(-2, 10), B=(-2, 7), and C=(-6, 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: (11.500, 1.000)


Question:
Given triangle ABC with coordinates A=(-8, 2), B=(4, -10), and C=(-2, 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: (-8.000, 2.000)


Question:
Consider triangle ABC with coordinates A=(3, -3), B=(9, 4), and C=(1, 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: 2.286


Question:
Given triangle ABC with coordinates A=(-5, 9), B=(-10, 9), and C=(-3, -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: (-3.000, 9.875)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, -2), B=(-8, 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: 1.844


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-7, 3), B=(-2, 8), and C=(2, 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: 1.644


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-7, 10), B=(3, 2), 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: 0.695


Question:
Given triangle ABC with coordinates A=(9, 0), B=(-9, -5), and C=(-2, 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: (-2.931, 8.352)


Question:
For triangle with vertices A=(2, -10), B=(6, -8), and C=(9, -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: (-15.000, 41.000)


Question:
Given triangle ABC with coordinates A=(-5, 4), B=(-7, 9), and C=(8, 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: (-5.310, 1.676)


Question:
Consider triangle ABC with coordinates A=(3, 2), B=(8, -1), and C=(10, -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: 1.019


Question:
Given a triangle with vertices A=(-7, -1), B=(7, 2), and C=(1, 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: 61.49°


Question:
In triangle ABC with coordinates A=(4, -2), B=(7, -3), and C=(8, 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: 76.76°


Question:
In triangle ABC with coordinates A=(7, 5), B=(-6, 7), 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: 27.18°


Question:
Given triangle ABC with coordinates A=(-1, -10), B=(0, -8), 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: (23.000, -8.000)


Question:
For triangle with vertices A=(-10, 0), B=(-4, 9), 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: (-8.500, 0.000)


Question:
Consider triangle ABC with coordinates A=(-9, -7), B=(-4, -7), and C=(-1, -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: 0.843


Question:
In triangle ABC with coordinates A=(4, -5), B=(-8, 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: 14.74°


Question:
Consider triangle ABC with coordinates A=(1, 9), B=(-3, 9), and C=(-2, -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: 1.633


Question:
Consider triangle ABC with coordinates A=(-3, -2), B=(-4, -4), 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: 0.992


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-10, 6), B=(8, 9), and C=(8, -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: 3.785


Question:
In triangle ABC with coordinates A=(-8, -9), B=(2, -1), and C=(-9, 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: 48.96°


Question:
Consider triangle ABC with coordinates A=(1, -7), B=(-1, -6), and C=(-2, 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: 0.833


Question:
In triangle ABC with coordinates A=(-6, -6), B=(-1, 1), and C=(6, -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: 73.41°


Question:
For triangle with vertices A=(1, -2), B=(2, -7), 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: (3.000, -8.000)


Question:
Given a triangle with vertices A=(9, 9), B=(-2, 5), and C=(5, -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: 64.98°


Question:
Consider triangle ABC with coordinates A=(-1, -10), B=(0, 6), and C=(9, -8). 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: 3.685


Question:
Consider triangle ABC with coordinates A=(-5, 7), B=(10, 8), 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: 2.142


Question:
In triangle ABC with coordinates A=(4, -6), B=(-9, 10), and C=(3, -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: 5.40°


Question:
Consider triangle ABC with coordinates A=(-8, -5), B=(1, -9), 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: 3.625


Question:
For triangle with vertices A=(0, 1), B=(-8, -4), and C=(-7, -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: (-10.421, 4.474)


Question:
Given triangle ABC with coordinates A=(9, 5), B=(1, -9), 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: (-1.595, -2.946)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-9, 6), B=(4, -7), 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: 2.879


Question:
Given a triangle with vertices A=(-7, -10), B=(0, -10), 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: 78.69°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-6, -10), B=(-6, -4), and C=(4, 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: 1.941


Question:
Consider triangle ABC with coordinates A=(-10, -9), B=(-10, 3), and C=(10, -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: 4.450


Question:
In triangle ABC with coordinates A=(10, 5), B=(-8, 2), and C=(5, -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: 37.76°


Question:
For triangle with vertices A=(5, -8), B=(-9, 5), 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: (6.371, -1.831)


Question:
Consider triangle ABC with coordinates A=(-8, 6), B=(-4, 2), and C=(6, -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: 0.882


Question:
For triangle with vertices A=(5, 0), B=(7, 7), and C=(-6, -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: (24.180, -16.623)


Question:
Consider triangle ABC with coordinates A=(5, 2), B=(-3, -5), and C=(1, -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: 0.558


Question:
Given a triangle with vertices A=(-1, -7), B=(-10, -6), 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: 96.34°


Question:
For triangle with vertices A=(7, 8), B=(6, -8), and C=(-1, 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: (4.165, 6.677)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(0, -1), B=(3, -2), and C=(6, 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: 1.111


Question:
Given triangle ABC with coordinates A=(-8, -1), B=(-1, -3), and C=(-4, -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: (-5.385, -8.846)


Question:
For triangle with vertices A=(2, 9), B=(-6, 5), 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: (-2.250, 0.500)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(4, 9), B=(4, 3), 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: 0.485


Question:
Given triangle ABC with coordinates A=(-10, 10), B=(10, -2), and C=(0, -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: (-13.320, -23.200)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, -10), B=(-1, 5), and C=(-2, -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: 0.498


Question:
Given a triangle with vertices A=(3, -3), B=(-8, 2), 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: 24.44°


Question:
Consider triangle ABC with coordinates A=(7, 10), B=(9, 10), and C=(-4, -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: 0.742


Question:
Consider triangle ABC with coordinates A=(6, -10), B=(9, 2), and C=(3, 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: 2.254


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-3, -7), B=(-1, -5), and C=(-10, 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: 1.250


Question:
Given triangle ABC with coordinates A=(-4, -4), B=(2, -7), and C=(9, 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: (1.676, -6.649)


Question:
For triangle with vertices A=(5, 10), B=(-6, 2), and C=(-9, -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: (-29.800, 21.600)


Question:
Given triangle ABC with coordinates A=(8, -6), B=(5, 1), and C=(-9, -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: (5.115, -0.951)


Question:
Consider triangle ABC with coordinates A=(1, -1), B=(0, -8), and C=(-1, -8). 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: 0.456


Question:
Given triangle ABC with coordinates A=(2, 7), B=(5, 2), 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: (2.000, -0.400)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, 7), B=(10, 8), 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: 0.352


Question:
In triangle ABC with coordinates A=(-10, 2), B=(8, 10), and C=(10, -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: 74.78°


Question:
In triangle ABC with coordinates A=(4, 4), B=(3, 2), and C=(10, -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: 120.96°


Question:
Given triangle ABC with coordinates A=(0, 7), B=(-2, 4), 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: (-0.091, 6.727)


Question:
For triangle with vertices A=(9, 6), B=(4, -8), 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: (2.690, -4.818)


Question:
Given a triangle with vertices A=(-6, 2), B=(-10, -5), and C=(4, 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: 33.69°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(5, -10), B=(2, 9), 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: 2.192


Question:
Given a triangle with vertices A=(0, -8), B=(8, 9), and C=(7, 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: 19.80°


Question:
Given a triangle with vertices A=(-8, 2), B=(-5, -10), 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: 75.96°


Question:
Given triangle ABC with coordinates A=(5, 7), B=(-8, -4), and C=(6, -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: (2.049, -3.330)


Question:
Consider triangle ABC with coordinates A=(-5, 7), B=(9, -3), and C=(-3, -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: 2.756


Question:
Given triangle ABC with coordinates A=(-3, -9), B=(10, -10), and C=(-5, -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: (-5.947, -15.316)


Question:
For triangle with vertices A=(-7, -1), B=(-4, -6), and C=(-6, -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: (-46.000, -27.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(5, 2), B=(-8, -10), 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: 2.427


Question:
For triangle with vertices A=(2, -9), B=(8, -8), and C=(-5, 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: (-1.421, -11.471)


Question:
Consider triangle ABC with coordinates A=(-1, -2), B=(3, 10), 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: 0.461


Question:
Given triangle ABC with coordinates A=(1, -5), B=(-6, 6), 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: (1.278, -0.550)


Question:
In triangle ABC with coordinates A=(-8, 10), B=(-1, 4), and C=(0, 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: 149.04°


Question:
For triangle with vertices A=(-4, 10), B=(4, -9), 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: (-8.065, -8.290)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(0, -9), B=(-10, 1), 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: 0.352


Question:
Given triangle ABC with coordinates A=(-9, 3), B=(-6, -1), and C=(1, 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: (-6.765, -4.824)


Question:
Given triangle ABC with coordinates A=(-10, 10), B=(7, 4), 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: (3.066, 1.686)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, -2), B=(1, 9), and C=(1, 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: 1.284


Question:
Given a triangle with vertices A=(3, -9), B=(-1, -5), and C=(7, 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: 103.39°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-6, -7), B=(6, -10), and C=(-1, 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: 3.365


Question:
Consider triangle ABC with coordinates A=(7, 6), B=(6, 6), and C=(10, 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: 0.121


Question:
Consider triangle ABC with coordinates A=(8, -1), B=(6, 4), and C=(-4, -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: 2.100


Question:
Given a triangle with vertices A=(5, 3), B=(-6, 4), 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: 12.16°


Question:
In triangle ABC with coordinates A=(9, -1), B=(3, 10), and C=(8, 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: 30.43°


Question:
In triangle ABC with coordinates A=(8, 0), B=(-2, -8), and C=(-10, -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: 148.47°


Question:
In triangle ABC with coordinates A=(-5, 4), B=(0, -9), 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: 7.26°


Question:
For triangle with vertices A=(-6, -5), B=(5, 0), and C=(1, 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: (-0.667, 5.667)


Question:
For triangle with vertices A=(-5, 5), B=(-2, -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: (-2.000, 5.300)


Question:
In triangle ABC with coordinates A=(1, 0), B=(-9, -5), and C=(-2, 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: 8.97°


Question:
For triangle with vertices A=(6, 0), B=(6, 10), 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: (22.000, 2.000)


Question:
For triangle with vertices A=(-10, -9), B=(7, 1), and C=(-10, 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: (-7.059, 1.000)


Question:
Given a triangle with vertices A=(10, -1), B=(5, -3), and C=(6, 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: 58.74°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(2, 5), B=(9, 10), and C=(8, 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: 0.885


Question:
In triangle ABC with coordinates A=(-7, 1), B=(-1, -10), and C=(-9, 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: 6.81°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, 8), B=(-2, 1), and C=(6, 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: 1.886


Question:
Given a triangle with vertices A=(9, 10), B=(-6, -10), and C=(-10, 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: 48.18°


Question:
Given a triangle with vertices A=(-5, -4), B=(7, -7), and C=(8, -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: 94.40°


Question:
In triangle ABC with coordinates A=(4, 2), B=(-7, 0), and C=(10, -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: 20.31°


Question:
Consider triangle ABC with coordinates A=(9, -5), B=(0, -4), and C=(-1, -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: 0.387


Question:
Consider triangle ABC with coordinates A=(3, 9), B=(-3, -3), 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: 0.664


Question:
Given triangle ABC with coordinates A=(-5, 5), B=(-1, 8), 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: (-1.724, 6.966)


Question:
Consider triangle ABC with coordinates A=(6, 8), B=(4, -2), and C=(10, 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: 2.112


Question:
Given a triangle with vertices A=(-1, 10), B=(1, -3), and C=(10, 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: 80.31°


Question:
In triangle ABC with coordinates A=(1, -5), B=(10, 1), 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: 41.28°


Question:
Given triangle ABC with coordinates A=(-6, 1), B=(-4, 2), 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: (-4.737, 1.474)


Question:
Consider triangle ABC with coordinates A=(8, 1), B=(-10, -4), and C=(-9, -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: 1.043


Question:
For triangle with vertices A=(-2, -1), B=(-2, 0), and C=(5, -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: (-2.000, -1.000)


Question:
Consider triangle ABC with coordinates A=(-2, 2), B=(8, 3), and C=(-2, -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: 1.872


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 8), B=(-6, 5), 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: 3.798


Question:
In triangle ABC with coordinates A=(3, 5), B=(-8, -7), and C=(-2, 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: 5.64°


Question:
Given a triangle with vertices A=(3, -4), B=(-5, -6), and C=(-7, 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: 84.09°


Question:
In triangle ABC with coordinates A=(7, -1), B=(3, 3), and C=(-7, -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: 87.27°


Question:
For triangle with vertices A=(4, -7), B=(-6, -3), and C=(5, -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: (4.059, -6.353)


Question:
For triangle with vertices A=(4, -6), B=(0, 3), and C=(1, 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: (-22.727, -1.545)


Question:
For triangle with vertices A=(-4, -6), B=(9, -5), 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: (3.800, -2.400)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-7, 10), B=(10, -4), and C=(-6, 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: 2.255


Question:
For triangle with vertices A=(-2, -1), B=(-6, -7), and C=(-10, 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: (-2.324, -1.118)


Question:
In triangle ABC with coordinates A=(-3, 7), B=(8, 10), and C=(6, -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: 69.03°


Question:
Consider triangle ABC with coordinates A=(2, -4), B=(3, -5), and C=(5, -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: 0.592

sqrt(-sqrt(2) + sqrt(5))*sqrt(sqrt(2) + sqrt(5))*sqrt(-sqrt(5) + 2*sqrt(2))/sqrt(sqrt(5) + 2*sqrt(2))


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, 1), B=(-2, 8), and C=(-2, 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: 0.725


Question:
In triangle ABC with coordinates A=(4, -10), B=(0, -3), and C=(-6, -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: 138.18°


Question:
For triangle with vertices A=(-9, 2), B=(2, -6), 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: (1.565, -0.348)


Question:
For triangle with vertices A=(-10, -1), B=(-2, 3), and C=(-5, 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: (14.000, -37.000)


Question:
Given triangle ABC with coordinates A=(-3, 2), B=(9, -10), and C=(-6, -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: (-4.077, -6.077)


Question:
In triangle ABC with coordinates A=(-1, 6), B=(2, -5), and C=(5, -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: 105.26°


Question:
For triangle with vertices A=(-10, 8), B=(-2, 5), and C=(0, -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: (6.980, 10.612)


Question:
In triangle ABC with coordinates A=(-7, 5), B=(-5, -5), and C=(9, -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: 109.44°


Question:
For triangle with vertices A=(-4, -5), B=(-9, -1), and C=(2, 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: (-3.898, -5.373)


Question:
Consider triangle ABC with coordinates A=(0, -5), B=(0, -3), 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: 0.083


Question:
Given triangle ABC with coordinates A=(8, -1), B=(-7, 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: (5.462, 9.154)


Question:
Given a triangle with vertices A=(-6, -3), B=(4, -4), and C=(3, -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: 39.29°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-7, 7), B=(-3, 9), 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: 1.978


Question:
In triangle ABC with coordinates A=(-6, 4), B=(8, 1), and C=(3, 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: 38.10°


Question:
Given triangle ABC with coordinates A=(10, 9), B=(-6, -8), and C=(5, 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: (41.593, -34.441)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-5, 1), B=(-2, 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: 1.209


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, -4), B=(4, 6), and C=(-6, -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: 3.407


Question:
Given triangle ABC with coordinates A=(3, 2), B=(8, 2), and C=(-6, -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: (-6.000, 16.000)


Question:
Given a triangle with vertices A=(-4, 10), B=(7, 7), 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: 15.26°


Question:
Given a triangle with vertices A=(4, -3), B=(-3, -9), and C=(4, 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: 24.38°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, -9), B=(2, -9), and C=(-5, -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: 1.002


Question:
Consider triangle ABC with coordinates A=(-4, 7), B=(-9, -6), and C=(1, -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: 3.235


Question:
Given a triangle with vertices A=(9, 1), B=(-10, 4), and C=(0, 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: 35.54°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-10, 4), B=(2, -6), and C=(-5, 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: 2.375


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-7, -5), B=(3, -4), 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: 2.877


Question:
In triangle ABC with coordinates A=(-6, -8), B=(4, 9), and C=(-5, -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: 8.82°


Question:
In triangle ABC with coordinates A=(-2, -7), B=(-1, 9), and C=(7, -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: 39.60°


Question:
For triangle with vertices A=(10, 10), B=(-9, -3), 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: (4.061, -6.628)


Question:
Given triangle ABC with coordinates A=(-2, 2), B=(2, -9), 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, 2.364)


Question:
For triangle with vertices A=(-8, -2), B=(0, 5), 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: (-19.167, 20.333)


Question:
Given triangle ABC with coordinates A=(-9, 6), B=(-6, -8), and C=(2, 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: (-6.000, 4.286)


Question:
Given a triangle with vertices A=(-4, 5), B=(-5, 7), and C=(5, -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: 13.24°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(5, -4), B=(1, -9), 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: 1.442


Question:
Given a triangle with vertices A=(10, -3), B=(-10, -4), and C=(-3, 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: 32.68°


Question:
For triangle with vertices A=(-8, 6), B=(2, -9), and C=(-3, 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: (26.571, 21.714)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-10, 4), B=(-6, 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: 0.438


Question:
In triangle ABC with coordinates A=(0, -5), B=(1, -4), 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: 139.09°


Question:
For triangle with vertices A=(-2, -5), B=(-6, 7), and C=(-7, -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: (-3.625, -4.875)


Question:
Given a triangle with vertices A=(5, -4), B=(10, 8), and C=(4, 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: 48.95°


Question:
For triangle with vertices A=(6, -7), B=(7, 9), 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: (279.000, -7.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-2, 7), B=(-9, 6), 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: 2.336


Question:
Given triangle ABC with coordinates A=(9, 3), B=(0, 1), and C=(6, -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: (4.800, -0.600)


Question:
Given a triangle with vertices A=(-9, 5), B=(4, -10), 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: 59.35°


Question:
In triangle ABC with coordinates A=(6, -4), B=(-5, 7), and C=(-1, -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: 25.02°


Question:
In triangle ABC with coordinates A=(1, -7), B=(-9, -4), and C=(-7, 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: 88.26°


Question:
Given a triangle with vertices A=(-1, 10), B=(-10, -5), and C=(-8, 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: 12.53°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-4, 0), B=(-9, -1), and C=(3, 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: 0.082


Question:
In triangle ABC with coordinates A=(5, 0), B=(2, 3), and C=(3, 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: 26.57°


Question:
Consider triangle ABC with coordinates A=(7, -1), B=(-6, 3), 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: 0.674


Question:
For triangle with vertices A=(0, 5), B=(-8, 8), and C=(-1, 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: (-1.818, 1.818)


Question:
Given triangle ABC with coordinates A=(-9, 7), B=(5, -2), and C=(2, -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: (0.200, -6.800)


Question:
Given a triangle with vertices A=(7, -9), B=(0, -9), and C=(0, -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: 90.00°


Question:
For triangle with vertices A=(-4, -10), B=(0, -9), and C=(-10, -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: (-6.947, -14.211)


Question:
Given triangle ABC with coordinates A=(-2, -7), B=(9, 3), and C=(-9, -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: (5.444, -21.889)


Question:
For triangle with vertices A=(2, -2), B=(-2, 9), and C=(-2, 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: (-29.500, -2.000)


Question:
Given a triangle with vertices A=(10, -2), B=(-3, -8), and C=(2, 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: 46.79°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, 7), B=(-7, -1), 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: 0.815


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-9, 2), B=(-7, 3), and C=(5, 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: 0.424


Question:
Given a triangle with vertices A=(8, 5), B=(-4, -10), 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: 11.53°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(1, -8), B=(0, 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: 0.974


Question:
Consider triangle ABC with coordinates A=(-5, 8), B=(2, 1), and C=(8, 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: 1.370


Question:
Find the incircle radius of triangle ABC whose vertices are A=(2, 5), B=(-6, 10), and C=(0, -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: 2.805


Question:
In triangle ABC with coordinates A=(6, -1), B=(-8, 10), and C=(-1, 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: 38.16°


Question:
Given a triangle with vertices A=(-10, -5), B=(-1, -1), 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: 84.47°


Question:
Given triangle ABC with coordinates A=(-7, -3), B=(4, -5), 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: (2.250, -7.625)


Question:
Given a triangle with vertices A=(-7, -1), B=(-6, 8), and C=(10, 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: 99.92°


Question:
In triangle ABC with coordinates A=(-2, -6), B=(-8, 5), and C=(-1, 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: 91.13°


Question:
For triangle with vertices A=(-8, -4), B=(4, 9), and C=(1, 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: (16.281, -13.105)


Question:
In triangle ABC with coordinates A=(-2, -7), B=(9, 1), and C=(-8, 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: 49.27°


Question:
Given a triangle with vertices A=(0, -9), B=(10, 7), 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: 1.68°


Question:
In triangle ABC with coordinates A=(2, -1), B=(-3, -10), and C=(0, 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: 19.05°


Question:
Given triangle ABC with coordinates A=(0, 10), B=(-3, -1), 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: (1.299, 4.373)


Question:
Given triangle ABC with coordinates A=(-9, 7), B=(5, 2), and C=(3, 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: (-0.750, -9.500)


Question:
In triangle ABC with coordinates A=(2, 6), B=(-7, 4), and C=(-6, -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: 97.77°


Question:
For triangle with vertices A=(4, 6), B=(-5, -8), and C=(-6, -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: (-14.400, 1.400)


Question:
Consider triangle ABC with coordinates A=(1, 1), B=(-8, 5), and C=(2, 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: 0.987


Question:
For triangle with vertices A=(5, 9), B=(-4, -1), and C=(-9, -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: (-106.273, 78.545)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(1, 10), B=(6, 3), 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: 3.324


Question:
Consider triangle ABC with coordinates A=(0, 4), B=(9, -10), 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: 1.005


Question:
For triangle with vertices A=(-6, -2), B=(3, -7), 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: (2.644, -5.842)


Question:
For triangle with vertices A=(4, 6), B=(-7, 4), and C=(1, 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: (1.367, -1.020)


Question:
Given a triangle with vertices A=(-9, 0), B=(-7, 8), and C=(3, -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: 44.50°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(1, 10), B=(4, -6), and C=(9, -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: 1.917


Question:
For triangle with vertices A=(8, 7), B=(-9, -7), and C=(4, 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: (50.828, -54.862)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-5, 0), B=(6, -1), and C=(4, 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: 3.179