Question:
In triangle ABC with coordinates A=(-8, 5), B=(-5, 9), and C=(7, -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: 87.06°


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

Answer: 2.784


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

Answer: (-2.176, -1.176)


Question:
Consider triangle ABC with coordinates A=(2, 5), B=(-4, -4), 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: 1.143


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

Answer: (38.000, 22.000)


Question:
In triangle ABC with coordinates A=(9, -3), B=(9, -8), 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: 43.03°


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

Answer: (-2.881, 4.017)


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

Answer: 47.73°


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

Answer: (10.308, -15.923)


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

Answer: 57.43°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(5, -1), B=(1, -4), and C=(-9, 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: 2.012


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

Answer: 60.26°


Question:
Given triangle ABC with coordinates A=(8, -7), B=(-5, 0), 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: (6.701, -2.127)


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


Question:
Consider triangle ABC with coordinates A=(-6, -8), B=(0, -10), and C=(5, -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: 1.925


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

Answer: (-6.400, 0.000)


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

Answer: 2.60°


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

Answer: 3.092


Question:
Consider triangle ABC with coordinates A=(10, 10), B=(2, 5), and C=(-8, 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: 1.948


Question:
Given triangle ABC with coordinates A=(10, -8), B=(-1, 4), and C=(-5, 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: (79.000, 84.000)


Question:
Given a triangle with vertices A=(9, -1), B=(6, 2), 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: 29.74°


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

Answer: 63.90°


Question:
For triangle with vertices A=(-2, 8), B=(1, -8), and C=(-2, -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: (-39.333, -8.000)


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

Answer: 95.19°


Question:
Given a triangle with vertices A=(-9, 2), B=(-5, -9), 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: 31.87°


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

Answer: (-4.800, 6.600)


Question:
Given a triangle with vertices A=(9, 4), B=(10, -8), and C=(9, -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: 4.70°


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

Answer: 2.329


Question:
Given a triangle with vertices A=(-1, -4), B=(7, 3), and C=(10, -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: 69.37°


Question:
For triangle with vertices A=(-10, 5), B=(8, 0), and C=(0, 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: (-107.500, -385.000)


Question:
Given triangle ABC with coordinates A=(-1, -8), B=(8, -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: (-2.000, 0.000)


Question:
For triangle with vertices A=(-1, 0), B=(5, -9), 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: (-45.000, -25.667)


Question:
Given a triangle with vertices A=(8, -4), B=(6, -7), 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: 29.60°


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

Answer: 40.10°


Question:
Given a triangle with vertices A=(10, 4), B=(-8, -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: 53.02°


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

Answer: 8.13°


Question:
In triangle ABC with coordinates A=(0, 3), B=(10, -6), and C=(0, -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: 36.28°


Question:
Consider triangle ABC with coordinates A=(1, 2), B=(-8, 9), and C=(-5, -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: 3.405


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

Answer: (1.391, -13.435)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-6, 9), B=(1, 7), and C=(9, -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: 2.049


Question:
In triangle ABC with coordinates A=(0, 4), B=(-8, 2), 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: 26.57°


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

Answer: (20.000, 27.000)


Question:
In triangle ABC with coordinates A=(3, -6), B=(9, 1), 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: 79.14°


Question:
Given a triangle with vertices A=(-6, -8), B=(-7, -4), and C=(-1, 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: 120.96°


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

Answer: 3.101


Question:
For triangle with vertices A=(6, -8), B=(-1, -8), and C=(9, 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: (9.000, -10.500)


Question:
In triangle ABC with coordinates A=(7, 4), B=(-3, -2), and C=(5, -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: 45.00°


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

Answer: 2.232


Question:
In triangle ABC with coordinates A=(-7, 6), B=(10, 6), 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: 59.74°


Question:
In triangle ABC with coordinates A=(8, -5), B=(7, 6), and C=(-10, -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: 55.72°


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

Answer: 1.527


Question:
Given a triangle with vertices A=(4, 2), B=(-9, 0), 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: 47.56°


Question:
For triangle with vertices A=(3, -5), B=(-9, 9), 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: (-4.344, -7.295)


Question:
In triangle ABC with coordinates A=(-6, 10), B=(-8, 9), 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: 31.76°


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

Answer: 2.522


Question:
For triangle with vertices A=(-6, -3), B=(-3, 0), 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: (-19.333, 2.333)


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

Answer: 3.799


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

Answer: 1.915


Question:
Consider triangle ABC with coordinates A=(-4, -4), B=(9, -2), 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: 3.713


Question:
Given a triangle with vertices A=(-3, 7), B=(-6, -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: 33.98°


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

Answer: (0.000, 13.600)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(0, 10), B=(-4, -3), and C=(-4, -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: 0.363


Question:
Given triangle ABC with coordinates A=(10, -2), B=(5, -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: (2.480, 7.400)


Question:
For triangle with vertices A=(-2, 1), 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: (-86.000, -76.000)


Question:
Given a triangle with vertices A=(1, -10), B=(9, -8), and C=(-8, 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: 57.30°


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

Answer: 3.045


Question:
Given triangle ABC with coordinates A=(-4, 3), B=(-4, 4), 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: (-2.800, 1.000)


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

Answer: (-0.043, -4.609)


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

Answer: (-9.000, -10.538)


Question:
Given triangle ABC with coordinates A=(-3, 2), B=(-2, 3), 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: (-14.000, 3.000)


Question:
Given triangle ABC with coordinates A=(8, -9), B=(-5, 7), 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: (-41.000, -33.500)


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

Answer: 30.07°


Question:
Given a triangle with vertices A=(2, -6), B=(3, 4), and C=(-8, 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: 108.73°


Question:
Consider triangle ABC with coordinates A=(-5, -4), B=(-2, 1), and C=(3, 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: 0.389


Question:
Consider triangle ABC with coordinates A=(9, 5), B=(-3, 3), and C=(2, 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: 0.570


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

Answer: 0.116


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, -5), B=(-9, -1), 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: 2.779


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

Answer: 23.06°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(8, 10), B=(10, 4), and C=(0, -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: 2.086


Question:
Given a triangle with vertices A=(-1, -4), B=(-5, -10), 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: 16.99°


Question:
Given a triangle with vertices A=(3, 7), B=(7, -8), and C=(-3, -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: 53.27°


Question:
Given triangle ABC with coordinates A=(5, 0), B=(4, -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: (4.250, -1.125)


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

Answer: (68.000, 42.000)


Question:
In triangle ABC with coordinates A=(-7, -4), B=(3, 7), 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: 42.53°


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

Answer: (-6.887, 1.132)


Question:
Consider triangle ABC with coordinates A=(7, -8), B=(-1, -8), and C=(2, -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: 0.492


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

Answer: 1.501


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

Answer: 1.464


Question:
Given a triangle with vertices A=(-7, 7), B=(3, -4), 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: 34.14°


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

Answer: (-65.000, -46.000)


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

Answer: 0.912


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

Answer: 3.974


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-4, -9), B=(-1, 7), and C=(8, 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: 3.414


Question:
In triangle ABC with coordinates A=(-9, 10), B=(7, -1), and C=(0, 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: 17.62°


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

Answer: 161.81°


Question:
Consider triangle ABC with coordinates A=(-5, -4), B=(-7, 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: 0.361


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-1, -5), B=(-4, -2), and C=(-1, 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: 1.328


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

Answer: (0.852, -1.074)


Question:
Given a triangle with vertices A=(-7, 1), B=(-8, 5), 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: 10.74°


Question:
Given a triangle with vertices A=(6, 6), B=(2, 7), and C=(8, 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: 23.50°


Question:
Given a triangle with vertices A=(10, -7), B=(5, -6), and C=(-8, 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: 142.22°


Question:
Consider triangle ABC with coordinates A=(-4, 1), B=(-10, 5), and C=(3, 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: 2.299


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

Answer: (-7.000, 0.000)


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

Answer: 93.58°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, -7), B=(8, -7), and C=(-3, -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: 0.042


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

Answer: (-36.000, 20.000)


Question:
In triangle ABC with coordinates A=(-9, -2), B=(-1, -2), and C=(-2, 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: 84.81°


Question:
Given triangle ABC with coordinates A=(4, 10), B=(-5, -1), 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: (-8.696, 0.478)


Question:
Given triangle ABC with coordinates A=(1, -10), B=(0, -1), 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: (-1.193, -0.133)


Question:
Given triangle ABC with coordinates A=(-8, -6), B=(7, 0), and C=(9, 8), find the coordinates of its orthocenter. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: (17.111, -12.278)


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

Answer: (72.000, 249.000)


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

Answer: (-0.656, -2.688)


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

Answer: 3.284


Question:
Find the incircle radius of triangle ABC whose vertices are A=(4, -1), B=(-2, -5), 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: 0.411


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

Answer: (9.364, 3.182)


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

Answer: 37.27°


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

Answer: 1.795


Question:
For triangle with vertices A=(-4, -8), B=(7, 2), 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: (-3.244, 1.069)


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

Answer: 90.00°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(7, 1), B=(-3, 4), 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: 2.059


Question:
Consider triangle ABC with coordinates A=(-7, 9), B=(7, 6), 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: 2.838


Question:
Find the incircle radius of triangle ABC whose vertices are A=(2, 7), B=(3, 8), 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: 0.663


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-9, -3), B=(4, -10), and C=(-4, 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: 3.824


Question:
Given triangle ABC with coordinates A=(9, -5), B=(-1, -5), and C=(-3, 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: (-3.000, -7.182)


Question:
In triangle ABC with coordinates A=(4, 0), B=(-8, -7), and C=(-9, -6), find the measure (in degrees) of angle ABC. For all geometry problems:
1. Give coordinates in the form (x, y)
2. Round decimal answers to 3 decimal places
3. Use the degree symbol ° for angles
4. Return only the angle, coordinates, or radius as your answer.

Answer: 104.74°


Question:
Given triangle ABC with coordinates A=(-10, 5), B=(-8, 6), 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: (-3.714, 12.429)


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

Answer: 41.78°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-2, -10), B=(3, -5), 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: 1.089


Question:
Find the incircle radius of triangle ABC whose vertices are A=(-5, -6), B=(2, -4), and C=(9, -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: 1.803


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

Answer: 3.782


Question:
In triangle ABC with coordinates A=(-10, -3), B=(-2, -9), 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: 75.75°


Question:
For triangle with vertices A=(-1, 5), B=(6, 2), 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: (-0.941, 5.471)


Question:
Consider triangle ABC with coordinates A=(2, 7), B=(1, 7), and C=(-5, 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: 0.196


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

Answer: 0.975


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

Answer: 0.670


Question:
Given triangle ABC with coordinates A=(0, -4), B=(-7, -3), 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: (1.895, -5.737)


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

Answer: (-5.500, 0.500)


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

Answer: 90.00°


Question:
Given triangle ABC with coordinates A=(3, 9), B=(1, -8), and C=(2, 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: (-38.538, 11.769)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(4, 5), B=(-6, 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: 3.505


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

Answer: (1.421, 14.526)


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

Answer: (47.571, -15.286)


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

Answer: (-3.000, -6.000)


Question:
For triangle with vertices A=(-7, -8), B=(7, 5), 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: (-1.375, -11.750)


Question:
Find the incircle radius of triangle ABC whose vertices are A=(9, 2), B=(10, -2), 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: 1.538


Question:
Given a triangle with vertices A=(-1, 9), B=(6, -5), 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: 31.33°


Question:
For triangle with vertices A=(3, 9), B=(-5, 10), 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: (-3.511, 7.915)


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

Answer: 1.74°


Question:
Find the incircle radius of triangle ABC whose vertices are A=(10, 7), B=(3, -5), 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: 1.347


Question:
In triangle ABC with coordinates A=(-4, -2), B=(4, -8), and C=(10, -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: 143.13°


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

Answer: (-8.000, -188.000)


Question:
Given a triangle with vertices A=(4, -6), B=(-2, -5), and C=(-8, -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: 136.85°


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

Answer: 0.380


Question:
For triangle with vertices A=(4, 5), B=(-7, -9), 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: (-9.816, 0.855)


Question:
Given triangle ABC with coordinates A=(-8, -2), B=(-6, -7), and C=(1, 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: (-11.458, 0.017)


Question:
In triangle ABC with coordinates A=(-5, -4), B=(-7, -9), 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: 1.82°


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

Answer: 0.410


Question:
Consider triangle ABC with coordinates A=(-5, 4), B=(2, -10), 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: 2.058