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

Answer: (0.000, -9.500)


Question:
For triangle with vertices A=(-4, 2), B=(1, 8), 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: (1.000, 2.000)


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

Answer: (11.000, 0.000)


Question:
Given a triangle with vertices A=(-9, 1), B=(3, 1), and C=(-6, 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: 18.43°


Question:
In triangle ABC with coordinates A=(-8, -7), B=(-6, 0), and C=(-9, -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: 15.02°


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

Answer: (6.756, -2.171)


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

Answer: 25.05°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(3, -1), B=(-1, 1), and C=(0, -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: 1.303


Question:
In triangle ABC with coordinates A=(1, 10), B=(-6, 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: 26.57°


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

Answer: (7.310, 5.972)


Question:
Consider triangle ABC with coordinates A=(-6, -7), B=(6, 4), 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: 0.996


Question:
Consider triangle ABC with coordinates A=(-3, 9), B=(-4, -8), and C=(8, -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: 4.187


Question:
For triangle with vertices A=(2, -8), B=(-5, -6), and C=(-1, 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: (-2.440, -5.040)


Question:
Given triangle ABC with coordinates A=(4, 6), B=(7, -5), and C=(0, 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: (7.000, 7.909)


Question:
Given a triangle with vertices A=(5, 4), B=(-2, 0), and C=(-8, 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: 91.22°


Question:
Consider triangle ABC with coordinates A=(-5, 4), B=(-7, 0), and C=(-5, -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: 0.971


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

Answer: 30.15°


Question:
For triangle with vertices A=(3, 6), B=(5, 9), 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: (-9.651, 3.767)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 9), B=(6, 1), 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: 1.772


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-9, 5), B=(10, -1), and C=(-10, 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: 1.508


Question:
Given triangle ABC with coordinates A=(2, -5), B=(-8, 2), and C=(8, -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: (-482.000, -709.000)


Question:
For triangle with vertices A=(-9, -3), B=(-4, -1), and C=(8, -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: (-6.000, 33.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-2, 9), B=(9, -8), and C=(-2, 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: 1.828


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

Answer: 0.991


Question:
Consider triangle ABC with coordinates A=(8, -7), B=(-6, -3), 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: 0.432


Question:
Consider triangle ABC with coordinates A=(-8, 7), B=(7, -7), and C=(4, -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: 0.653


Question:
Given triangle ABC with coordinates A=(0, 5), B=(8, -10), and C=(9, -1), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (16.759, 3.138)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-6, 6), B=(-8, 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: 0.032


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

Answer: 0.445


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

Answer: 0.530


Question:
For triangle with vertices A=(1, -9), B=(1, -10), and C=(-8, -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: (1.000, -10.000)


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

Answer: (-1.048, 23.667)


Question:
Consider triangle ABC with coordinates A=(1, 8), B=(4, -2), 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: 0.550


Question:
For triangle with vertices A=(-10, -5), B=(6, 6), and C=(2, 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: (200.000, -285.000)


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

Answer: 1.544


Question:
Given a triangle with vertices A=(-3, 5), B=(1, 2), and C=(-8, -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: 78.50°


Question:
Given a triangle with vertices A=(9, 2), B=(10, -6), and C=(1, -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: 106.84°


Question:
For triangle with vertices A=(4, -5), B=(-9, 1), 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: (-11.714, -20.714)


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

Answer: 1.958


Question:
Given a triangle with vertices A=(-2, 3), B=(6, 8), and C=(5, -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: 54.42°


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

Answer: 105.95°


Question:
Consider triangle ABC with coordinates A=(0, 3), B=(-7, 9), 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: 2.212


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

Answer: (-4.714, 12.286)


Question:
Given a triangle with vertices A=(8, 0), B=(6, 9), and C=(-4, 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: 91.22°


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

Answer: 17.59°


Question:
Given a triangle with vertices A=(-5, 8), B=(0, 7), and C=(-3, -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: 89.22°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-3, 1), B=(4, 9), and C=(9, -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: 3.668


Question:
Consider triangle ABC with coordinates A=(-5, 2), B=(4, 4), and C=(5, -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: 2.557


Question:
Given triangle ABC with coordinates A=(8, -6), B=(-9, -7), 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: (-2.615, -32.538)


Question:
Given triangle ABC with coordinates A=(6, 8), B=(6, 5), and C=(1, -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: (47.600, -8.000)


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

Answer: 35.13°


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

Answer: 45.00°


Question:
Given triangle ABC with coordinates A=(-4, -1), B=(-10, -10), 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: (17.000, -10.000)


Question:
In triangle ABC with coordinates A=(4, 8), B=(-7, -9), and C=(7, 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: 12.09°


Question:
In triangle ABC with coordinates A=(-9, -9), B=(-10, -2), and C=(-7, -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: 15.07°


Question:
For triangle with vertices A=(-1, -8), B=(10, 6), 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: (2.282, -9.436)


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

Answer: 25.35°


Question:
Given triangle ABC with coordinates A=(10, 2), B=(-2, -8), and C=(-5, -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: (0.370, -12.444)


Question:
Given triangle ABC with coordinates A=(3, -1), B=(-8, 7), 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: (-9.679, -6.434)


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

Answer: 68.96°


Question:
Given a triangle with vertices A=(9, -7), B=(4, -7), and C=(10, 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: 65.22°


Question:
Given a triangle with vertices A=(6, 5), B=(10, 8), 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: 19.52°


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

Answer: 58.74°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(2, 3), B=(-1, 6), and C=(-10, 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: 0.925


Question:
Given triangle ABC with coordinates A=(7, 3), B=(3, 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: (7.000, -15.000)


Question:
Consider triangle ABC with coordinates A=(-7, -10), B=(3, -5), and C=(-9, -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: 2.100


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 6), B=(5, 10), 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: 2.310


Question:
Given a triangle with vertices A=(1, -4), B=(3, -6), 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: 37.87°


Question:
Given a triangle with vertices A=(-6, 2), B=(4, 2), and C=(0, -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: 71.57°


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

Answer: (6.477, -0.890)


Question:
Given a triangle with vertices A=(1, 4), B=(2, -5), 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: 57.09°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, -8), B=(-6, 10), and C=(-5, -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: 1.088


Question:
For triangle with vertices A=(1, 2), B=(-1, 10), 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: (-12.538, -5.385)


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

Answer: (8.364, 5.364)


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

Answer: 42.88°


Question:
Given triangle ABC with coordinates A=(-9, -10), B=(-6, 8), and C=(-7, 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: (-101.000, 20.667)


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

Answer: 112.83°


Question:
Given a triangle with vertices A=(5, 8), B=(-6, 6), and C=(7, 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: 31.34°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(0, -7), B=(4, 2), 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: 3.378


Question:
Given a triangle with vertices A=(-3, -4), B=(8, -9), and C=(2, 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: 46.12°


Question:
Consider triangle ABC with coordinates A=(-9, -2), B=(-4, -6), and C=(-7, 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: 1.830


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 3), B=(6, 7), and C=(4, -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: 1.644


Question:
Consider triangle ABC with coordinates A=(-8, -3), B=(-10, -1), and C=(9, -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: 0.474


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

Answer: 33.56°


Question:
Consider triangle ABC with coordinates A=(-6, 9), B=(5, 10), 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: 3.426


Question:
In triangle ABC with coordinates A=(-2, -4), B=(-8, -10), and C=(4, -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: 30.96°


Question:
Given a triangle with vertices A=(-5, 0), B=(-10, 5), and C=(8, 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: 51.34°


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

Answer: 0.436


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

Answer: 50.60°


Question:
For triangle with vertices A=(10, -6), B=(7, 4), and C=(6, -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: (4.649, -5.405)


Question:
Consider triangle ABC with coordinates A=(-3, 8), B=(1, -6), and C=(1, -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: 0.432


Question:
Given a triangle with vertices A=(-1, -9), B=(-9, -2), and C=(1, 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: 72.15°


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

Answer: 1.498


Question:
For triangle with vertices A=(-3, 4), B=(10, 9), and C=(5, -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: (3.321, 1.366)


Question:
For triangle with vertices A=(7, -9), B=(-2, -8), and C=(0, 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: (-1.291, -7.618)


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

Answer: 1.183


Question:
Consider triangle ABC with coordinates A=(-3, 10), B=(-9, 7), and C=(-8, -6). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 2.219


Question:
Given triangle ABC with coordinates A=(-4, 4), B=(-4, 6), and C=(9, 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: (-5.846, 0.000)


Question:
In triangle ABC with coordinates A=(-2, 5), B=(-7, -7), 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: 20.41°


Question:
For triangle with vertices A=(-6, -10), B=(-2, -4), 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: (26.000, -14.000)


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

Answer: (-9.710, 5.097)


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

Answer: 131.82°


Question:
Consider triangle ABC with coordinates A=(-10, -1), B=(-1, 3), 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: 1.871


Question:
Given a triangle with vertices A=(-2, 6), B=(8, 7), 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: 72.19°


Question:
Given triangle ABC with coordinates A=(9, 10), B=(0, 6), and C=(7, 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: (7.174, 3.609)


Question:
For triangle with vertices A=(10, 1), B=(-1, -6), 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: (5.728, 1.570)


Question:
Given a triangle with vertices A=(-2, -9), B=(-3, -7), 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: 116.57°


Question:
Consider triangle ABC with coordinates A=(7, 4), B=(-4, 4), 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: 1.387


Question:
In triangle ABC with coordinates A=(5, 2), B=(3, 1), and C=(-3, 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: 135.00°


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

Answer: 1.454


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

Answer: 3.219


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

Answer: (-52.333, -63.333)


Question:
In triangle ABC with coordinates A=(-8, -6), B=(-3, -8), and C=(-9, 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: 48.76°


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

Answer: (3.833, -2.083)


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

Answer: (19.667, 9.000)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(10, -3), B=(5, 3), 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: 1.993


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-7, -5), B=(6, -2), and C=(9, 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: 1.511


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

Answer: 41.82°


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

Answer: (4.535, 1.907)


Question:
In triangle ABC with coordinates A=(-6, -5), B=(-1, 7), and C=(3, -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: 46.58°


Question:
In triangle ABC with coordinates A=(-5, -4), B=(-2, -4), and C=(-2, -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: 90.00°


Question:
Given a triangle with vertices A=(-1, -9), B=(-7, -1), and C=(-4, 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: 106.26°


Question:
Given triangle ABC with coordinates A=(5, -9), B=(-10, 7), and C=(7, 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: (9.778, 2.605)


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

Answer: 2.170


Question:
In triangle ABC with coordinates A=(-5, 6), B=(-9, 5), and C=(-5, 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: 30.96°


Question:
For triangle with vertices A=(4, 9), B=(7, 10), 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: (-18.609, 24.826)


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

Answer: 53.13°


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

Answer: 0.705


Question:
In triangle ABC with coordinates A=(-8, 7), B=(-7, -10), and C=(2, 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: 36.10°


Question:
In triangle ABC with coordinates A=(-7, 2), B=(10, 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: 64.80°


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

Answer: 1.320


Question:
In triangle ABC with coordinates A=(0, -2), B=(1, 7), and C=(10, -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: 43.21°


Question:
Consider triangle ABC with coordinates A=(-6, -10), B=(7, 5), and C=(-8, -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: 2.473


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

Answer: 0.862


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

Answer: (-4.000, 14.000)


Question:
For triangle with vertices A=(-8, -2), B=(-5, -6), and C=(10, -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: (-4.667, -12.000)


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

Answer: (13.688, -20.375)


Question:
In triangle ABC with coordinates A=(-9, -1), B=(-3, -5), 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: 55.49°


Question:
Given triangle ABC with coordinates A=(6, -10), B=(3, 4), and C=(1, -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: (-2.062, -8.656)


Question:
Consider triangle ABC with coordinates A=(-1, -6), B=(8, -7), and C=(9, 10). Compute the radius of its incircle. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 3.426


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

Answer: 16.27°


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

Answer: 2.858


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

Answer: (9.638, -0.241)


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

Answer: 2.267


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

Answer: 0.671


Question:
For triangle with vertices A=(-5, 0), B=(-1, 2), and C=(-9, 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: (-1.000, -16.000)


Question:
Consider triangle ABC with coordinates A=(4, 10), B=(-5, 3), and C=(0, 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: 1.166


Question:
Consider triangle ABC with coordinates A=(3, -6), B=(-3, 4), and C=(8, -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: 1.362


Question:
In triangle ABC with coordinates A=(6, -7), B=(0, 3), and C=(7, 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: 35.84°


Question:
In triangle ABC with coordinates A=(-9, 0), B=(2, -8), and C=(10, -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: 107.10°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, 0), B=(-5, -9), and C=(7, -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: 2.771


Question:
Given triangle ABC with coordinates A=(5, -6), B=(10, -5), and C=(-7, -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: (22.429, -154.143)


Question:
Given a triangle with vertices A=(2, 0), B=(-1, -8), 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: 20.56°


Question:
Consider triangle ABC with coordinates A=(-2, 9), B=(9, 1), and C=(-7, -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: 4.476


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, -5), B=(4, -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: 0.806


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-8, 6), 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: 0.230


Question:
For triangle with vertices A=(7, -8), B=(0, -4), and C=(4, -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: (-8.000, -28.000)


Question:
For triangle with vertices A=(-7, 0), B=(-7, -4), 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: (-3.000, 2.000)


Question:
Given triangle ABC with coordinates A=(9, -3), B=(9, -2), and C=(8, 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: (15.000, 0.000)


Question:
In triangle ABC with coordinates A=(1, -5), B=(2, -3), and C=(-8, 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: 80.13°


Question:
Given a triangle with vertices A=(-10, 5), B=(-7, -9), 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: 93.35°


Question:
In triangle ABC with coordinates A=(-5, -8), B=(3, 10), and C=(6, 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: 44.52°


Question:
Given triangle ABC with coordinates A=(5, -3), B=(3, -2), and C=(-5, -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: (1.143, 7.286)


Question:
Consider triangle ABC with coordinates A=(-3, 1), B=(-2, 0), 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: 0.547


Question:
Given a triangle with vertices A=(-7, -7), B=(10, 5), and C=(-4, 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: 31.13°


Question:
Given triangle ABC with coordinates A=(-2, 4), B=(-1, -3), and C=(5, -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: (-7.923, -7.846)


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

Answer: (29.222, 21.833)


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

Answer: 2.366


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-6, -5), B=(4, 2), 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: 1.859


Question:
For triangle with vertices A=(7, 0), B=(-9, -4), and C=(-6, 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: (-9.000, 12.000)


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

Answer: (8.600, 7.000)


Question:
Consider triangle ABC with coordinates A=(-10, -7), B=(8, 5), 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: 2.836


Question:
Consider triangle ABC with coordinates A=(-10, -5), B=(10, 3), 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: 4.061


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 3), B=(-7, 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: 1.050


Question:
Given triangle ABC with coordinates A=(4, 4), B=(1, 8), and C=(-2, 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: (3.556, 4.167)


Question:
For triangle with vertices A=(1, -6), B=(1, -4), 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: (-111.000, 10.000)


Question:
Given a triangle with vertices A=(7, -5), B=(2, 6), and C=(-4, -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: 58.13°


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

Answer: (4.828, -4.310)


Question:
For triangle with vertices A=(-3, 2), B=(-6, 0), 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: (-2.304, 2.957)


Question:
Given a triangle with vertices A=(-7, -2), B=(0, 6), and C=(1, 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: 67.75°


Question:
In triangle ABC with coordinates A=(9, -4), B=(-4, 4), and C=(2, -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: 13.39°


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

Answer: 2.818


Question:
Given a triangle with vertices A=(-7, -5), B=(2, -10), and C=(-6, 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: 36.98°


Question:
Consider triangle ABC with coordinates A=(-9, -2), B=(10, -4), and C=(-5, 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: 4.034


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

Answer: 1.795


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

Answer: 45.00°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(10, -9), B=(5, -6), and C=(2, 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: 1.511


Question:
In triangle ABC with coordinates A=(-1, 4), B=(-8, 5), 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: 19.44°


Question:
Given a triangle with vertices A=(-4, 9), B=(-10, -4), 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: 76.53°


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

Answer: 12.99°


Question:
Given a triangle with vertices A=(-2, -7), B=(7, -10), 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: 51.01°


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

Answer: 2.333


Question:
Find the incircle radius of triangle ABC whose vertices are A=(4, 5), B=(-5, -1), 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: 1.953


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

Answer: 2.94°


Question:
In triangle ABC with coordinates A=(2, -6), B=(-8, 5), 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: 47.73°


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

Answer: 1.758


Question:
Given triangle ABC with coordinates A=(10, 2), B=(5, -10), 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: (5.000, -2.167)


Question:
Given a triangle with vertices A=(5, 8), B=(-9, 5), 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: 7.70°


Question:
For triangle with vertices A=(9, -8), B=(-6, 0), 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: (17.556, 17.667)


Question:
Given a triangle with vertices A=(-6, 7), B=(1, 0), and C=(-1, -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: 113.20°


Question:
Given triangle ABC with coordinates A=(-5, 5), B=(6, 3), and C=(-7, -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: (-5.391, 5.848)


Question:
Consider triangle ABC with coordinates A=(4, -8), B=(0, -10), and C=(-8, -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: 1.566


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

Answer: 0.641


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-10, 8), B=(-1, 7), 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: 0.890


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

Answer: 1.534


Question:
Find the incircle radius of triangle ABC whose vertices are A=(4, 10), B=(-1, -6), 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: 1.826


Question:
Given triangle ABC with coordinates A=(2, -5), B=(9, -1), and C=(10, 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: (16.839, -7.968)


Question:
In triangle ABC with coordinates A=(8, 4), B=(-9, -5), and C=(10, -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: 18.92°


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

Answer: (-5.919, 8.297)


Question:
Given triangle ABC with coordinates A=(2, 9), B=(-1, 1), and C=(10, -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: (0.809, 2.447)


Question:
Given triangle ABC with coordinates A=(-10, 9), B=(9, 2), and C=(2, -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: (-0.240, -8.080)


Question:
In triangle ABC with coordinates A=(-6, -6), B=(-3, 10), and C=(-10, 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: 24.37°


Question:
Given triangle ABC with coordinates A=(-1, -9), B=(9, -1), and C=(0, 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: (4.545, -0.682)


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

Answer: (3.944, -3.028)


Question:
For triangle with vertices A=(9, 0), B=(1, -4), 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: (2.778, -1.556)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, 0), B=(7, 5), 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: 2.044


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-5, -6), B=(-1, 1), and C=(-6, -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: 1.456


Question:
For triangle with vertices A=(0, 6), B=(5, -7), 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: (-4.000, -3.000)


Question:
In triangle ABC with coordinates A=(10, 5), B=(-1, 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: 124.02°


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

Answer: (5.667, 14.667)


Question:
Consider triangle ABC with coordinates A=(9, -3), B=(-5, -8), 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: 1.922


Question:
In triangle ABC with coordinates A=(-6, 7), B=(1, -9), and C=(-6, -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: 66.37°


Question:
Consider triangle ABC with coordinates A=(10, -1), B=(8, -7), and C=(10, -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: 0.464


Question:
In triangle ABC with coordinates A=(10, -2), B=(5, 1), and C=(-6, -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: 124.59°


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

Answer: 2.791


Question:
For triangle with vertices A=(-6, -8), B=(-3, 8), 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: (-43.333, 8.000)


Question:
Given triangle ABC with coordinates A=(-1, 5), B=(-4, 8), and C=(-10, -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: (-2.800, 6.200)


Question:
Given triangle ABC with coordinates A=(-3, -2), B=(-2, 4), and C=(10, -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: (-8.698, -6.884)


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

Answer: (1.000, 6.375)


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

Answer: 54.08°


Question:
Given a triangle with vertices A=(9, -1), B=(1, 8), 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: 63.43°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-4, -3), B=(8, -5), and C=(7, -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: 0.996


Question:
Given a triangle with vertices A=(10, -4), B=(1, -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: 19.44°


Question:
Consider triangle ABC with coordinates A=(-10, 7), B=(10, -7), and C=(-10, -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: 5.047


Question:
In triangle ABC with coordinates A=(-2, 4), B=(-7, 8), and C=(-2, 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: 38.66°


Question:
Given a triangle with vertices A=(8, 0), B=(8, -1), and C=(-8, 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: 66.37°


Question:
In triangle ABC with coordinates A=(-7, -2), B=(10, -4), and C=(-3, 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: 18.07°


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

Answer: (4.000, 3.000)


Question:
Given a triangle with vertices A=(9, 2), B=(-4, 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: 65.22°


Question:
Given triangle ABC with coordinates A=(5, -5), B=(8, -8), and C=(0, 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: (-31.000, -21.000)


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

Answer: 2.62°


Question:
Given a triangle with vertices A=(6, 7), B=(-3, -7), and C=(9, 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: 4.13°


Question:
Given triangle ABC with coordinates A=(-1, 10), B=(-8, 7), 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: (-42.000, 92.000)


Question:
Given triangle ABC with coordinates A=(-7, 5), B=(-5, -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: (-7.000, -6.000)


Question:
Consider triangle ABC with coordinates A=(2, -5), B=(7, 8), 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: 0.840


Question:
Consider triangle ABC with coordinates A=(3, -7), B=(-10, -1), 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: 4.299


Question:
Given triangle ABC with coordinates A=(-9, -1), B=(0, -10), 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: (4.333, 7.333)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(4, -8), B=(6, 10), and C=(4, -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: 0.055


Question:
In triangle ABC with coordinates A=(2, -1), B=(4, 3), 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: 145.30°


Question:
In triangle ABC with coordinates A=(-9, 3), B=(5, 4), 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: 55.43°


Question:
Consider triangle ABC with coordinates A=(-1, -1), B=(1, 0), and C=(-7, -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: 0.106


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

Answer: 0.388


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

Answer: (30.667, -44.667)


Question:
For triangle with vertices A=(-3, 7), B=(-9, 9), and C=(-6, -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: (-3.000, 7.000)


Question:
Consider triangle ABC with coordinates A=(3, -4), B=(5, 4), and C=(-3, 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: 2.438


Question:
Given a triangle with vertices A=(6, -8), B=(1, -5), 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: 30.96°


Question:
Given a triangle with vertices A=(-3, -7), B=(-8, 10), and C=(9, -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: 25.43°


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

Answer: (-4.526, 5.263)


Question:
Consider triangle ABC with coordinates A=(4, -9), B=(-10, -6), and C=(-6, 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: 3.664


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

Answer: 51.48°


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

Answer: 83.48°


Question:
Consider triangle ABC with coordinates A=(5, -10), B=(1, -4), and C=(-6, 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: 0.306


Question:
Find the incircle radius of triangle ABC whose vertices are A=(6, 7), B=(-10, 4), and C=(10, -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: 4.883


Question:
Given triangle ABC with coordinates A=(-4, -10), 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: (-0.571, 3.714)


Question:
For triangle with vertices A=(10, 4), B=(1, -4), and C=(9, 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: (12.692, 1.846)


Question:
Consider triangle ABC with coordinates A=(-6, 0), B=(7, 6), and C=(-10, -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: 1.767


Question:
Consider triangle ABC with coordinates A=(2, -3), B=(9, -3), and C=(4, 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: 2.467


Question:
For triangle with vertices A=(4, 4), B=(-9, 1), 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: (-1.000, 9.000)


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

Answer: 0.833


Question:
In triangle ABC with coordinates A=(5, -6), B=(2, 3), and C=(5, 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: 130.60°


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

Answer: (-80.000, 71.000)


Question:
Given a triangle with vertices A=(-5, 1), B=(1, -10), and C=(-8, -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: 37.43°


Question:
Given a triangle with vertices A=(-2, 0), B=(3, 9), 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: 60.95°


Question:
In triangle ABC with coordinates A=(-10, -2), B=(4, 3), and C=(-9, -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: 20.58°


Question:
Given triangle ABC with coordinates A=(3, -5), B=(5, -2), and C=(9, 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: (62.400, -26.600)


Question:
In triangle ABC with coordinates A=(8, -1), B=(0, 2), 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: 52.74°


Question:
For triangle with vertices A=(7, 1), B=(-6, -10), and C=(-4, -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: (-22.333, 15.667)


Question:
For triangle with vertices A=(-8, -2), B=(9, -4), 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: (7.556, -9.778)


Question:
Given a triangle with vertices A=(0, -5), B=(4, 10), 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: 58.37°


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

Answer: (11.875, 10.000)


Question:
Given a triangle with vertices A=(-7, -5), B=(0, 8), and C=(6, -8), determine the angle at B in degrees. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 48.86°