messages
listlengths 1
1
| ground_truth
stringlengths 5
21
| dataset
stringclasses 1
value | type
stringclasses 1
value |
|---|---|---|---|
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 1), B=(8, 10), and C=(-8, 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"
}
] |
2.106
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-9, -2), B=(-9, 1), and C=(9, 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"
}
] |
1.259
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(6, 10), B=(1, 4), 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"
}
] |
(1.650, -0.875)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 8), B=(5, 2), 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"
}
] |
2.217
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-3, 10), B=(-9, 5), and C=(-3, -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"
}
] |
84.81°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-9, -6), B=(-4, 1), and C=(-5, -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"
}
] |
28.41°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(9, -9), B=(5, 9), and C=(9, -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"
}
] |
7.45°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-7, -1), B=(-4, 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"
}
] |
56.31°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(5, -4), B=(2, 1), and C=(-10, -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"
}
] |
94.40°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 6), B=(-4, 2), and C=(6, -1). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
0.882
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-9, 1), B=(6, -2), and C=(0, 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"
}
] |
33.69°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(3, -10), B=(-8, -3), 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"
}
] |
41.93°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(9, -10), B=(-6, 2), and C=(0, -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"
}
] |
17.65°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(9, -10), B=(-5, -10), and C=(-8, 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"
}
] |
(-8.000, -15.100)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-9, -9), B=(7, 3), 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"
}
] |
(7.000, -18.333)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-6, -10), B=(8, 6), and C=(4, 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"
}
] |
0.188
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-10, 7), B=(-4, 10), and C=(6, 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"
}
] |
(-1.692, 17.385)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(2, -4), B=(-3, -1), 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"
}
] |
0.053
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(3, 3), B=(8, -9), 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"
}
] |
(12.857, 12.857)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(10, -7), B=(5, -1), and C=(-8, 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"
}
] |
170.04°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(0, 3), B=(-7, 9), and C=(4, 8). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
2.212
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, -2), B=(-3, 9), and C=(0, 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"
}
] |
2.423
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(0, 0), B=(-7, -5), and C=(9, 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"
}
] |
3.53°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(7, 10), B=(-1, 5), 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"
}
] |
(37.889, -67.222)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-4, 8), B=(-3, -7), and C=(2, -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"
}
] |
(3.154, -3.923)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(8, -7), B=(5, 3), 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"
}
] |
(9.536, 8.361)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-6, 5), B=(-10, -5), and C=(-9, -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"
}
] |
0.807
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(10, -1), B=(5, -7), and C=(0, -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"
}
] |
0.995
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(2, 6), B=(0, 6), and C=(-4, -8), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
105.95°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-3, 3), B=(-10, -3), and C=(7, -10), 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"
}
] |
62.98°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 0), B=(-4, 9), and C=(-8, 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"
}
] |
1.294
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(0, 3), B=(-1, 1), and C=(7, -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"
}
] |
(-1.000, 1.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(4, -7), B=(-6, -3), and C=(5, -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"
}
] |
(4.059, -6.353)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-10, -2), B=(5, -4), and C=(-8, -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"
}
] |
16.34°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(6, 3), B=(2, -9), and C=(-2, 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"
}
] |
(-1.286, -0.238)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(10, -10), B=(4, -1), and C=(-6, 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"
}
] |
145.49°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-2, -5), B=(-6, -10), and C=(-6, 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"
}
] |
(1.500, -5.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(8, -9), B=(3, -9), and C=(1, 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"
}
] |
2.142
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 0), B=(-8, 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"
}
] |
1.103
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-2, 4), B=(10, -3), and C=(-1, 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"
}
] |
14.74°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-3, -4), B=(-7, -9), 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"
}
] |
(-8.870, 9.696)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-2, -3), B=(7, 1), and C=(0, -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"
}
] |
21.04°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, -7), B=(2, -3), and C=(-5, -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"
}
] |
1.508
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, -4), B=(-2, 9), 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"
}
] |
2.190
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(2, 5), B=(9, 10), and C=(10, 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"
}
] |
0.633
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-7, -4), B=(6, 6), and C=(9, 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"
}
] |
(105.667, -116.667)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, 3), B=(6, 7), and C=(4, -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"
}
] |
1.644
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, -4), B=(4, -7), 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"
}
] |
1.137
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(1, 0), B=(-9, -5), and C=(-2, 0), find the measure (in degrees) of angle ABC. For all geometry problems:\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"
}
] |
8.97°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(6, -10), B=(3, 4), and C=(1, -8), find the coordinates of its orthocenter. For all geometry problems:\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"
}
] |
(-2.062, -8.656)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-4, 5), B=(-4, -2), and C=(-7, -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"
}
] |
1.245
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(8, -7), B=(1, 2), 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"
}
] |
(-7.500, -12.167)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(9, -7), B=(0, -4), 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"
}
] |
(-8.905, -13.714)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-5, -9), B=(-8, 5), and C=(10, -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"
}
] |
59.47°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-4, -6), B=(3, -7), and C=(3, -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"
}
] |
(3.429, -6.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(5, -6), B=(-9, -6), 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"
}
] |
7.13°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-1, 0), B=(-5, 4), and C=(-6, -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"
}
] |
(2.714, -0.286)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-5, 5), B=(5, -2), 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"
}
] |
(0.758, -3.061)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(0, -5), B=(6, 2), 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"
}
] |
(5.049, -2.756)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-1, -3), B=(0, 2), and C=(-5, 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"
}
] |
(-1.957, -0.609)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -8), B=(4, -1), and C=(3, 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"
}
] |
0.633
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-7, 6), B=(-2, 2), and C=(6, 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"
}
] |
(-1.463, -0.328)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-1, -5), B=(9, 2), 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"
}
] |
2.974
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-10, -8), B=(-3, 8), 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"
}
] |
(4.431, -5.376)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(1, 0), B=(-1, 5), and C=(-10, -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"
}
] |
61.09°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(4, -10), B=(-9, -9), and C=(5, 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"
}
] |
45.00°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(5, -4), B=(10, 8), and C=(4, 6), determine the angle at B in degrees. For all geometry problems:\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"
}
] |
48.95°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(0, -4), B=(-3, -4), and C=(-7, -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"
}
] |
0.576
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(3, -10), B=(-5, 8), and C=(4, -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"
}
] |
15.33°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-5, 4), B=(3, -8), 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"
}
] |
(-1.643, -9.429)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-4, 9), B=(-1, -8), and C=(1, -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"
}
] |
31.81°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(4, -4), B=(7, 4), and C=(5, -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"
}
] |
(-9.588, -1.529)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-7, -7), B=(7, 4), and C=(3, -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"
}
] |
18.15°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(-6, 8), B=(-9, 4), and C=(0, -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"
}
] |
86.82°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "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:\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"
}
] |
41.78°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-3, -2), B=(-7, 7), and C=(-9, 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"
}
] |
(-3.000, 9.667)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(5, -3), B=(-3, -5), and C=(-10, 10), 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"
}
] |
100.98°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-10, 6), B=(-2, -1), and C=(3, 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"
}
] |
2.431
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(1, -5), B=(-6, 6), and C=(10, 5), find the coordinates of its orthocenter. For all geometry problems:\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"
}
] |
(1.278, -0.550)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(5, 5), B=(4, 1), and C=(-4, -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"
}
] |
(19.840, -11.960)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(6, 8), B=(7, -6), and C=(-2, -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"
}
] |
56.86°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(7, 9), B=(8, -10), 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"
}
] |
11.02°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-7, -1), B=(6, -4), and C=(0, -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"
}
] |
(-3.677, -20.935)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(4, 1), B=(3, -9), and C=(-4, -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"
}
] |
(5.710, -10.971)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(-5, -6), B=(9, 8), and C=(4, -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"
}
] |
(9.000, -11.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(9, -7), B=(3, 5), 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"
}
] |
(3.944, -3.028)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(5, -9), B=(-6, 1), 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"
}
] |
(4.116, -2.372)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-7, -1), B=(2, 2), and C=(2, 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"
}
] |
(5.000, -1.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-3, 1), B=(-4, 5), and C=(-8, 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"
}
] |
(-3.238, 1.190)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(1, 3), B=(-8, 2), and C=(10, -6). Compute the radius of its incircle. For all geometry problems:\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"
}
] |
2.170
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(2, -4), B=(-8, 5), and C=(9, 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"
}
] |
55.23°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "In triangle ABC with coordinates A=(5, -6), B=(2, 3), and C=(5, 8), find the measure (in degrees) of angle ABC. For all geometry problems:\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"
}
] |
130.60°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(5, -9), B=(-10, 7), and C=(7, 0), find the coordinates of its orthocenter. For all geometry problems:\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"
}
] |
(9.778, 2.605)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 8), B=(-7, -5), and C=(0, -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"
}
] |
2.227
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given triangle ABC with coordinates A=(1, -9), B=(8, -1), and C=(4, 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"
}
] |
(10.328, -1.537)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-2, -2), B=(-5, 0), 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"
}
] |
7.94°
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 10), B=(-8, -7), and C=(6, 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"
}
] |
3.881
|
Puzzle
|
advanced_geometry
|
[
{
"content": "For triangle with vertices A=(-2, 2), B=(-7, -1), and C=(5, 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"
}
] |
(-46.000, 90.000)
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Consider triangle ABC with coordinates A=(-10, -6), B=(-3, 6), and C=(-8, -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"
}
] |
0.358
|
Puzzle
|
advanced_geometry
|
[
{
"content": "Given a triangle with vertices A=(-10, -1), B=(-10, 6), and C=(10, -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"
}
] |
68.20°
|
Puzzle
|
advanced_geometry
|
Subsets and Splits
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