messages
listlengths 1
1
| ground_truth
stringlengths 5
21
| dataset
stringclasses 1
value | type
stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Given triangle ABC with coordinates A=(6, 9), B=(5, 7), and C=(8, -3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-7.750, 4.875)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-7, -8), B=(4, -8), and C=(-6, -5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-6.000, -4.667)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-7, 8), B=(6, -7), and C=(1, -9), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(0.109, -9.772)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(9, -5), B=(4, 0), and C=(10, -7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(30.000, 13.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-7, -9), B=(0, 0), and C=(-4, -1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
38.09°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-10, -3), B=(5, -2), and C=(-4, -1), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-6.167, 31.500)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(8, 1), B=(0, -2), and C=(0, -1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
69.44°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(7, 5), B=(6, 3), and C=(6, -3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-10.000, 5.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-9, 0), B=(-1, 2), and C=(-3, -7), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-4.500, -1.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-7, 0), B=(8, -6), and C=(-8, -9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-6.170, -4.426)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-9, -7), B=(4, -2), and C=(-4, -5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.48°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-1, -3), B=(-6, -10), and C=(8, 7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-151.385, 120.846)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 3), B=(10, 6), and C=(-6, 0). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.541
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-1, 5), B=(7, 4), and C=(-9, -9), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-6.417, 11.667)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-10, 4), B=(5, -7), and C=(-2, -4). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.853
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, -2), B=(-9, -7), and C=(-9, 10). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
4.731
|
Puzzle
|
advanced_geometry
|
[
{
"content": "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:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(47.571, -15.286)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(7, 5), B=(2, -7), and C=(4, -10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.222
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 9), B=(1, -4), and C=(-7, 6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
2.314
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(0, 4), B=(-4, -1), and C=(-4, -8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
141.34°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(8, -3), B=(4, -3), and C=(8, -5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(8.000, -3.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(6, 8), B=(-8, -6), and C=(-1, 9), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
19.98°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -4), B=(-1, 3), and C=(-5, -9). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
2.789
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-1, -5), B=(-9, 2), and C=(0, 8), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
74.88°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-6, 8), B=(3, 3), and C=(-2, 7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(8.909, 26.636)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(7, -2), B=(-6, 0), and C=(-3, -10), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-2.194, -4.758)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(4, 1), B=(9, -6), and C=(5, -5). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.223
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-6, -9), B=(8, -8), and C=(0, 1), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(0.313, -3.388)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(6, 5), B=(-2, 10), and C=(-7, 0). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
3.040
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(6, 10), B=(-1, -3), and C=(-6, 10). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
3.834
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-9, -10), B=(1, -9), and C=(2, -4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(2.837, -12.367)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 7), B=(10, 8), and C=(0, -2). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.352
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(2, 6), B=(10, 3), and C=(-8, -6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-1.143, 12.286)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-9, -5), B=(0, -6), and C=(-10, -10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
28.14°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(6, 9), B=(5, -2), and C=(3, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-3.600, 6.600)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(5, 6), B=(-1, -5), and C=(-5, -2), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-2.161, -3.548)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-4, 1), B=(10, -6), and C=(1, 4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(2.364, 6.727)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, -9), B=(8, 9), and C=(0, -6). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.934
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, -3), B=(5, -9), and C=(-7, 9). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
3.671
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 10), B=(7, 8), and C=(9, -9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
4.511
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(0, 10), B=(-6, 4), and C=(3, 2), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-0.909, 5.909)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(9, 5), B=(-8, 1), and C=(1, -4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
3.040
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, -6), B=(6, -1), and C=(1, -6). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.914
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-6, -2), B=(-3, 6), and C=(-3, -4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-8.333, -2.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(9, 3), B=(4, 1), and C=(-8, -9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.622
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-6, -9), B=(7, -9), and C=(5, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(5.000, -7.533)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 6), B=(9, 1), and C=(-9, 9). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.856
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(10, 6), B=(8, 8), and C=(-2, 6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.959
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-5, 3), B=(-8, 7), and C=(-5, -3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
20.17°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-1, 7), B=(6, -5), and C=(-4, -6), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
65.45°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(8, 10), B=(-2, -9), and C=(5, 3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(158.462, -77.769)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-6, -1), B=(2, -6), and C=(-9, -1), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
7.56°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-10, 0), B=(-4, -1), and C=(3, 7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(0.327, -9.036)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-5, 10), B=(-6, 3), and C=(5, -9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
129.36°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "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:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-7.923, -7.846)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(3, -1), B=(6, -10), and C=(-7, -6), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
54.46°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 5), B=(9, 10), and C=(8, 7). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.885
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(3, -3), B=(1, -6), and C=(-3, -5). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.996
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(0, -9), B=(10, 7), and C=(6, 1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.68°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(5, 0), B=(-7, -10), and C=(1, -5). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.636
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(7, 2), B=(-9, -3), and C=(-10, -3), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
162.65°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 7), B=(-9, 4), and C=(9, 2). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.994
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(6, -2), B=(10, -3), and C=(7, -4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.735
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(5, -10), B=(-4, 4), and C=(-8, 5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
136.77°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "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:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
2.836
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, -2), B=(2, 3), and C=(2, -8). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.496
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-4, 7), B=(-5, -3), and C=(10, 8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
48.04°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(4, 10), B=(9, 3), and C=(-2, 7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
34.48°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(3, 7), B=(-7, -3), and C=(-10, -3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(3.000, -16.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(5, 6), B=(-5, 0), and C=(10, 7), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-14.600, 48.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-4, -10), B=(-9, 4), and C=(-8, 8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-36.000, -2.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(1, 8), B=(0, -10), and C=(-5, -8). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
2.272
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-9, 4), B=(0, -5), and C=(5, -6). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
1.028
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 10), B=(6, 3), and C=(-10, -3). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
3.324
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(5, 6), B=(8, 5), and C=(1, -4), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
70.56°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(9, -3), B=(0, -8), and C=(-4, 0), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(0.130, -7.435)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-2, 8), B=(5, -10), and C=(-5, -8), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
57.44°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "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:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
2.267
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(3, 10), B=(6, 1), and C=(-5, 1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
71.57°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-4, -8), B=(3, -10), and C=(3, 2), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
74.05°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(4, 7), B=(-2, -8), and C=(-1, -6), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
4.76°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-3, 1), B=(0, 5), and C=(0, -2), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
36.87°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(4, 0), B=(7, 7), and C=(2, 5), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
45.00°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(1, 6), B=(2, 7), and C=(-6, -8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-44.000, 30.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(8, 7), B=(10, -9), and C=(-5, 6), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(8.714, 7.714)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, -1), B=(-5, 0), and C=(6, 8). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.382
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(0, 0), B=(-8, 4), and C=(-8, -4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-6.000, 0.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-2, -3), B=(-10, 8), and C=(3, 9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
58.37°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-3, -7), B=(-8, -10), and C=(3, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-3.000, 0.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(1, 7), B=(-5, 4), and C=(-4, -9), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
112.17°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-3, 6), B=(0, -4), and C=(7, 0), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(1.390, -1.683)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(1, 4), B=(2, -2), and C=(10, -5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-3.200, -7.200)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-6, 9), B=(-8, -10), and C=(-1, 3), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(6.636, 2.196)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-6, 3), B=(-3, -5), and C=(2, 6), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
45.00°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-6, 7), B=(2, 7), and C=(9, 8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(9.000, -98.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 5), B=(0, 2), and C=(1, 2). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
0.158
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(10, 10), B=(-9, -3), and C=(5, -8), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(4.061, -6.628)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(9, 10), B=(6, -5), and C=(9, -6), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(4.000, -5.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(8, 1), B=(-1, 10), and C=(-6, 10), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
135.00°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(4, -5), B=(-8, -6), and C=(-7, -7), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] |
(-6.308, -15.308)
|
Puzzle
|
advanced_geometry
|
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