messages
listlengths 1
1
| ground_truth
stringlengths 5
21
| dataset
stringclasses 1
value | type
stringclasses 1
value |
|---|---|---|---|
[
{
"content": "For triangle with vertices A=(-5, -6), B=(-3, 3), and C=(-8, 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"
}
] |
(-6.535, 1.674)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, -7), B=(-6, 6), and C=(7, -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"
}
] |
3.865
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(2, 8), B=(-10, 9), and C=(-1, 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"
}
] |
7.77°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 4), B=(8, 6), and C=(5, -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"
}
] |
3.809
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-2, -10), B=(2, -10), and C=(-4, -4), 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"
}
] |
(-4.000, -12.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(3, 9), B=(-3, -3), and C=(1, 2). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
0.664
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(9, 0), B=(-4, -2), and C=(-7, -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"
}
] |
125.31°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-10, -8), B=(-10, 3), 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"
}
] |
60.26°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, 5), B=(5, -6), and C=(10, -1). 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"
}
] |
2.366
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(9, 9), B=(-2, 5), and C=(5, -2), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
64.98°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-6, 2), B=(0, 8), and C=(-3, -4), 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"
}
] |
(-10.000, 3.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-8, 9), B=(3, -7), and C=(0, 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"
}
] |
(3.000, 11.062)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(6, 6), B=(-8, 0), and C=(9, -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"
}
] |
(4.430, 2.664)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 10), B=(-9, 7), and C=(-8, -6). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
2.219
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(7, 3), B=(6, 10), and C=(2, -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"
}
] |
24.08°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "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:\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"
}
] |
60.26°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-3, 4), B=(3, 0), and C=(2, 3), 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"
}
] |
37.87°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-6, 7), B=(-6, 3), and C=(-10, -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"
}
] |
(13.250, -4.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(8, 9), B=(-6, 6), and C=(-9, -1). 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"
}
] |
2.137
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-4, -4), B=(2, -7), and C=(9, 8), find the coordinates of its orthocenter. For all geometry problems:\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"
}
] |
(1.676, -6.649)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -4), B=(-6, 2), and C=(-5, 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"
}
] |
1.573
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(1, -1), B=(-8, -1), and C=(9, 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"
}
] |
27.90°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 2), B=(-4, 0), and C=(-4, 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"
}
] |
1.323
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-1, 0), B=(8, -8), and C=(-7, -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"
}
] |
3.553
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(0, -2), B=(2, -10), and C=(-9, 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"
}
] |
16.03°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(7, -7), B=(1, -1), and C=(7, -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"
}
] |
(9.000, -1.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, -2), B=(6, -9), and C=(3, -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"
}
] |
0.223
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-10, -3), B=(-8, 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"
}
] |
(-7.118, 4.412)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-4, 5), B=(-3, 2), and C=(-3, -7). 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"
}
] |
0.372
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(2, 7), B=(-5, 1), and C=(-8, -4), 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"
}
] |
161.57°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(5, 8), B=(1, -7), and C=(10, 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"
}
] |
(9.835, 4.044)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(10, -10), B=(3, -7), 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"
}
] |
121.94°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(6, 6), B=(10, -7), and C=(5, -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"
}
] |
(-1.132, -5.887)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(1, 0), B=(5, -1), and C=(-9, -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"
}
] |
46.77°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-3, -4), B=(8, -9), and C=(2, 8), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
46.12°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(2, 1), B=(-4, -5), and C=(2, 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"
}
] |
8.13°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(10, -5), B=(1, -6), and C=(6, -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"
}
] |
17.65°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-4, 4), B=(9, 3), 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"
}
] |
(6.756, -3.171)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(6, -4), B=(5, 2), and C=(10, 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"
}
] |
(6.897, 0.483)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(0, -9), B=(7, -3), and C=(-2, 3). 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"
}
] |
2.981
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 8), B=(-9, -5), 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"
}
] |
2.747
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-10, -8), B=(4, -1), 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"
}
] |
4.831
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(0, -3), B=(-7, -6), and C=(-9, 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"
}
] |
73.93°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-9, 6), B=(-8, -5), and C=(-2, 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"
}
] |
(-4.676, 2.757)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 3), B=(-10, 2), and C=(-7, -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"
}
] |
0.970
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(8, -7), B=(-6, -3), and C=(-10, -3). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
0.432
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -10), B=(-1, 5), and C=(-2, -1). 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"
}
] |
0.498
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-3, 7), B=(8, 2), and C=(9, 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"
}
] |
110.56°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-10, -2), B=(-10, 7), and C=(-9, -3), find the coordinates of its orthocenter. For all geometry problems:\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"
}
] |
(-20.000, -3.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -9), B=(8, 2), and C=(9, 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"
}
] |
0.100
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-5, 0), B=(9, -9), and C=(-1, -3), 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"
}
] |
1.77°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-8, -9), B=(2, 7), and C=(-10, 0), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
27.74°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, -3), B=(5, 3), and C=(-6, 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"
}
] |
1.993
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(1, 2), B=(-2, -10), and C=(8, -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"
}
] |
(3.351, -5.838)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-7, 3), B=(8, 1), 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"
}
] |
(2.394, -4.045)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(9, -7), B=(3, 5), and C=(-8, 2). 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"
}
] |
3.405
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 6), B=(2, 2), and C=(2, -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"
}
] |
0.479
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-8, 10), B=(-9, 7), 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"
}
] |
129.56°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-2, -6), B=(-5, 10), and C=(8, 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"
}
] |
47.77°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(0, -8), B=(8, 9), and C=(7, 8), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
19.80°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(1, -1), B=(9, -3), 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"
}
] |
(-15.000, -31.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(9, 10), B=(-5, -6), and C=(9, 3), 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"
}
] |
(19.286, -6.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(2, 0), B=(-5, -7), 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"
}
] |
135.00°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-5, 6), B=(-5, 9), and C=(-1, 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"
}
] |
63.43°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-7, -6), B=(8, -8), and C=(9, 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"
}
] |
(7.505, -7.209)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-7, 3), B=(-7, -5), and C=(-2, -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"
}
] |
(-3.800, -1.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 9), B=(0, 0), and C=(7, -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"
}
] |
0.852
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(9, -7), B=(4, -7), and C=(10, 6), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
65.22°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-3, 4), B=(9, -9), and C=(-5, 5), 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"
}
] |
2.29°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-3, -7), B=(5, 1), and C=(8, 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"
}
] |
(1.500, 6.500)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, 2), B=(7, -5), and C=(-5, -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"
}
] |
2.622
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(7, -10), B=(4, 2), 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"
}
] |
(-3.333, 2.917)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 10), B=(-8, 3), and C=(-9, 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"
}
] |
1.436
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-4, 10), B=(7, 7), and C=(-10, 7), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
15.26°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(8, 0), B=(8, 3), and C=(-6, 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"
}
] |
1.341
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-5, 2), B=(4, 4), and C=(5, -4). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
2.557
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(1, 1), B=(-5, -8), and C=(4, -3). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
1.953
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-5, 3), B=(0, -4), and C=(-3, 5), 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"
}
] |
(-6.500, 2.500)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(2, -10), B=(3, 0), and C=(-1, -7). 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"
}
] |
1.476
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, 0), B=(7, 10), and C=(10, 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"
}
] |
0.840
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(1, 0), B=(5, -3), 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"
}
] |
73.74°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-4, -9), B=(7, -4), and C=(6, -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"
}
] |
1.485
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -3), B=(3, -3), and C=(-4, 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"
}
] |
1.243
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-4, -10), B=(-8, -9), and C=(5, 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"
}
] |
63.12°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, -8), B=(7, 2), and C=(8, -5). 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"
}
] |
2.358
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(10, -3), B=(1, 2), and C=(8, 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"
}
] |
(5.079, 2.742)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-6, 8), B=(-2, 9), and C=(-10, -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"
}
] |
1.550
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(8, -3), B=(-10, 8), and C=(2, -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"
}
] |
(1.043, -8.565)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-8, 5), B=(5, -7), and C=(9, 4), 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"
}
] |
67.27°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-5, -8), B=(-3, 4), and C=(-1, 1), find the measure (in degrees) of angle ABC. For all geometry problems:\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"
}
] |
43.15°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-2, -7), B=(-10, 9), and C=(-2, -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"
}
] |
1.51°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(9, -9), B=(10, 5), and C=(-9, 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"
}
] |
82.90°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-1, 10), B=(10, 7), and C=(9, -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"
}
] |
100.86°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-5, 8), B=(4, 6), and C=(3, 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"
}
] |
(4.149, 6.170)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-9, 9), B=(7, 3), and C=(7, -5). 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"
}
] |
2.762
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(6, 4), B=(-5, -9), and C=(-4, 4), 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"
}
] |
35.84°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(0, -10), B=(-5, -9), and C=(4, -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"
}
] |
1.186
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-3, 10), B=(3, 0), and C=(10, -4), 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"
}
] |
(-21.957, -23.174)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(2, 6), B=(7, -5), and C=(2, -3), 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"
}
] |
(-2.400, -5.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 0), B=(7, 5), 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"
}
] |
2.044
|
Puzzle
|
advanced_geometry
|
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