messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1 value | type stringclasses 1 value |
|---|---|---|---|
[
{
"content": "For triangle with vertices A=(2, -4), B=(-4, 4), and C=(7, 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"
}
] | (2.000, 0.250) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, 2), B=(-7, -5), 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"
}
] | (-7.000, 11.714) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-1, -1), B=(6, -5), and C=(-6, 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"
}
] | 0.036 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -5), B=(-9, -7), and C=(6, -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"
}
] | 10.84° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, 0), B=(5, -9), 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"
}
] | (-45.000, -25.667) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, 7), B=(-7, -2), and C=(0, 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"
}
] | (-21.333, 17.111) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(2, 10), B=(-5, -2), 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"
}
] | (4.755, -3.774) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 0), B=(8, 5), and C=(5, 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"
}
] | 1.056 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 1), B=(10, -6), and C=(5, 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"
}
] | (-6.000, -2.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-5, 4), B=(10, -7), and C=(9, 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"
}
] | 3.783 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 0), B=(-9, 0), and C=(-2, 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"
}
] | 29.74° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, -10), B=(-1, 1), and C=(-9, 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"
}
] | (1.283, 3.739) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(4, -5), B=(-5, 10), 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"
}
] | 0.423 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, 5), B=(-9, 6), and C=(-8, 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"
}
] | 1.801 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, 5), B=(1, 2), and C=(-8, -6), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 78.50° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, 3), B=(1, 5), and C=(1, 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, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 7), B=(9, 3), and C=(-3, -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"
}
] | 81.87° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(1, -2), B=(2, -7), and C=(-7, -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, -8.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 5), B=(6, 9), 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"
}
] | 1.268 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-3, -5), B=(-5, 2), 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"
}
] | 47.49° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 1), B=(10, -6), 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"
}
] | 1.417 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(0, -9), B=(-6, 8), 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"
}
] | (0.000, 6.235) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, -9), B=(1, 0), 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"
}
] | 2.146 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(5, 8), B=(-9, -4), and C=(-10, 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"
}
] | (-8.268, 6.979) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -5), B=(-3, -1), and C=(-5, 7). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 1.534 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, 7), B=(-4, 2), and C=(6, -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"
}
] | 109.23° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(9, -6), B=(-5, -2), and C=(-4, 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"
}
] | 1.416 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, -7), B=(3, -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"
}
] | 1.316 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, -8), B=(-9, 5), and C=(-7, 2). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius as your answer.\n",
"role": "user"
}
] | 0.862 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, -1), B=(-6, -1), and C=(0, 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"
}
] | 0.782 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 7), B=(9, 2), 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"
}
] | 1.325 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, 5), B=(10, -1), and C=(2, -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"
}
] | 54.40° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 2), B=(1, 4), and C=(1, -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"
}
] | 56.31° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, -1), B=(-9, 7), and C=(4, -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"
}
] | 18.54° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 6), B=(-8, 9), 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"
}
] | 0.827 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, -1), B=(-9, -10), 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"
}
] | 0.446 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, 5), B=(8, -7), and C=(7, -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"
}
] | (13.000, -2.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(5, 7), B=(10, 6), and C=(9, 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"
}
] | 0.098 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, 0), B=(-2, -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"
}
] | 85.60° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 4), B=(5, -2), and C=(2, -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"
}
] | 1.150 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -10), B=(7, 5), and C=(8, 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"
}
] | 172.87° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(3, 5), B=(-2, -8), and C=(-1, 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"
}
] | 0.951 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(10, -9), B=(-3, 9), and C=(8, -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"
}
] | 1.33° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -2), B=(7, -5), 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"
}
] | 28.86° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, 2), B=(0, 9), 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"
}
] | 80.54° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, 1), B=(-10, -10), 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"
}
] | 42.27° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-5, 10), B=(-4, 4), 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"
}
] | 30.34° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 0), B=(-10, -4), 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"
}
] | (-6.411, 4.203) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 2), B=(9, -5), 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"
}
] | 2.565 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, 3), B=(3, 5), and C=(-3, 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"
}
] | 27.90° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 3), B=(-2, -7), and C=(-7, -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"
}
] | 83.66° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, 2), B=(-10, 6), and C=(-4, -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"
}
] | 38.20° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(6, 3), B=(-10, 8), and C=(-8, 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"
}
] | 2.671 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(10, 8), B=(-9, 9), and C=(2, 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"
}
] | 0.210 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-5, 8), B=(6, 10), and C=(4, 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"
}
] | 46.01° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, -5), B=(-9, 2), and C=(-7, -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"
}
] | 0.270 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, -7), B=(10, -5), 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"
}
] | (10.000, -5.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, -8), B=(-2, 1), and C=(7, -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"
}
] | (-2.000, -19.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, 1), B=(6, -8), and C=(10, -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"
}
] | (-10.667, -29.667) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, -3), B=(0, -10), and C=(0, 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"
}
] | 0.986 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, 5), B=(1, 7), and C=(-3, -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"
}
] | (-21.455, 10.455) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(2, -8), B=(-5, -6), and C=(-1, 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"
}
] | (-2.440, -5.040) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 0), B=(-8, -8), and C=(3, -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"
}
] | 2.783 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(7, -1), B=(-4, 7), and C=(5, 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"
}
] | (20.529, 23.353) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, 6), B=(9, 6), and C=(-3, 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"
}
] | 18.43° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, -2), B=(10, 9), 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"
}
] | (-0.500, -12.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, -9), B=(4, -1), and C=(0, 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"
}
] | 90.00° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -6), B=(-1, -8), and C=(-5, -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"
}
] | (-11.000, -10.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, 5), B=(-3, 10), 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"
}
] | 2.947 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-5, 4), B=(-7, 9), 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"
}
] | (-5.310, 1.676) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, 2), B=(-3, 0), 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"
}
] | (3.111, -2.444) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -10), B=(-4, 6), and C=(9, 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"
}
] | 43.54° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, 8), B=(-4, 5), 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"
}
] | (0.377, 8.830) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-6, -1), B=(-2, 3), and C=(-9, -7), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 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, 20.000) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, 4), B=(-6, 1), 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"
}
] | (-4.909, 15.182) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 3), B=(3, -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"
}
] | 53.82° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, -7), B=(-9, -8), and C=(-10, 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"
}
] | (-8.924, -7.917) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, 4), B=(-9, 8), and C=(4, -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"
}
] | 8.13° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(9, -7), B=(-9, -2), and C=(-3, 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"
}
] | (-4.857, 1.314) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, 4), B=(-3, -2), and C=(5, -4), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 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=(-7, 9), B=(2, 0), 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"
}
] | (-2.412, 0.588) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(0, -5), B=(3, -5), and C=(6, -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"
}
] | 161.57° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(7, 9), B=(-6, 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"
}
] | 0.293 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 5), B=(8, -10), and C=(-8, 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"
}
] | (4.838, 1.856) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 1), B=(-5, -8), and C=(8, 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"
}
] | (-7.000, 0.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(7, 0), B=(-9, 3), and C=(-7, -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"
}
] | 65.34° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 4), B=(-9, -4), and C=(-6, -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"
}
] | 75.32° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, 8), B=(-5, -8), 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"
}
] | 3.558 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, 4), B=(8, 10), 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"
}
] | (-24.000, 34.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(10, -4), B=(0, 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"
}
] | 93.01° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, -1), B=(-5, -5), and C=(8, -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"
}
] | (-19.351, -30.514) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(7, 2), B=(-2, -4), 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"
}
] | (7.000, 2.000) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, -1), B=(-1, 1), and C=(0, -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"
}
] | 1.303 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, 0), B=(-7, -2), and C=(-1, 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"
}
] | 21.16° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(7, -8), B=(10, 2), 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"
}
] | 95.10° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(3, 1), B=(-7, -8), and C=(-3, -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"
}
] | 3.01° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-10, 5), B=(-1, -4), and C=(7, 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"
}
] | (-1.111, -2.111) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, -9), B=(-3, -8), and C=(-8, -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"
}
] | 0.808 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 5), B=(-4, 2), and C=(-2, -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"
}
] | 98.03° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, -4), B=(0, -7), and C=(-1, -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"
}
] | (2.143, -4.143) | Puzzle | advanced_geometry |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.