messages listlengths 1 1 | ground_truth stringlengths 5 21 | dataset stringclasses 1
value | type stringclasses 1
value |
|---|---|---|---|
[
{
"content": "In triangle ABC with coordinates A=(-7, 8), B=(-8, 2), 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, coordi... | 57.92° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(8, -10), B=(3, 3), and C=(2, 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, o... | 167.09° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-5, 8), B=(-10, 0), 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,... | (-18.667, 21.667) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-6, 10), B=(3, 7), and C=(2, -7), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 104.35° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(1, -6), B=(-1, 8), and C=(-1, -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, ... | 8.13° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(3, 10), B=(-6, -10), and C=(8, 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 radiu... | 2.742 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-4, -1), B=(0, -9), and C=(10, 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,... | (-1.750, -2.875) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-8, 4), B=(-3, 7), and C=(-8, -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 radiu... | 1.826 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(2, 3), B=(-9, -3), and C=(5, 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 ... | 1.023 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, 5), B=(-10, 9), and C=(-4, 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, ... | 25.41° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-9, 5), B=(-2, 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... | 113.86° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, -5), B=(-4, 4), 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, coordi... | (5.100, 4.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(2, 0), B=(6, -10), and C=(7, 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, o... | 24.66° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(8, 1), B=(7, -1), and C=(0, -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, c... | (16.000, -13.000) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(6, 10), B=(-10, -4), and C=(3, 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,... | 5.94° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, 9), B=(8, 4), and C=(-9, -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, coo... | 55.00° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-2, 1), B=(0, -9), 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, coordina... | 2.679 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, -4), B=(9, 1), 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, o... | 29.50° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, -5), B=(3, -7), and C=(-4, 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, coord... | 2.789 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 2), B=(3, -3), and C=(-3, -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, coordin... | 0.415 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, 9), B=(0, -7), and C=(2, 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, o... | 27.27° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, -8), B=(10, 5), and C=(0, 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 ... | 2.638 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, -5), B=(-7, 7), and C=(-10, 8), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates,... | 113.20° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-3, 3), B=(-8, -4), 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, coor... | 35.54° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, 10), B=(8, 4), and C=(1, -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 ... | 1.726 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-6, -4), B=(-4, 4), and C=(-6, -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 angl... | (-62.000, 4.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -1), B=(-5, 9), and C=(-10, 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, coord... | 1.353 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(3, 0), B=(9, -10), and C=(-1, -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, coor... | (3.615, 0.769) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, -7), B=(0, 1), 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, ... | (-4.400, 1.400) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, -6), B=(1, 7), and C=(4, 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, coordinat... | 1.186 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, -4), B=(9, 7), and C=(-2, -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, coordi... | 0.757 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(10, 2), B=(-2, -8), and C=(-5, -6), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coo... | (0.370, -12.444) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, -2), B=(-5, 6), and C=(8, -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, coor... | 59.04° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, -1), B=(4, 2), and C=(6, 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, co... | (3.000, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, 7), B=(9, -3), 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, coordin... | 21.37° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, -8), B=(3, -6), and C=(-9, -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, coor... | 125.54° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(4, -5), B=(-9, -6), 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,... | 59.04° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-10, 5), B=(4, -6), 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, coo... | 33.76° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, -8), B=(2, 6), 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, coordin... | (-46.000, 15.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 10), B=(-1, -3), and C=(-6, -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, coo... | 2.765 | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-10, 7), B=(-6, -5), 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, ... | 59.62° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(0, -6), B=(9, 8), and C=(8, -4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordi... | (12.766, -7.064) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, 0), B=(9, 8), and C=(-6, 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 ... | 2.464 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-3, 4), B=(-4, 3), 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, coordi... | 0.223 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, -5), B=(10, -9), and C=(7, 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, coord... | 34.38° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, 3), B=(-8, -6), and C=(10, -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, coo... | 2.990 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(9, -2), B=(-8, -4), 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, coo... | 59.84° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(4, -3), B=(-10, 3), and C=(-3, -10), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angl... | (-1.200, -5.800) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-4, 6), B=(-1, 9), 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... | 65.56° | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-7, -7), B=(10, 5), 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, ... | 31.13° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(1, -1), B=(-6, -6), and C=(10, -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, coo... | (1.000, 6.600) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 1), B=(-5, -7), and C=(4, 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, coor... | (-5.231, -3.769) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-8, 2), B=(-3, 10), 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,... | (-8.529, 1.706) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(5, 8), B=(-8, -5), and C=(-2, -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 radiu... | 1.992 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -10), B=(3, -5), and C=(-9, -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, coor... | 2.100 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-10, -8), B=(6, -9), and C=(-10, -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, coo... | 0.483 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-9, 0), B=(2, -8), and C=(10, -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, coor... | 107.10° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, -8), B=(6, 10), and C=(4, -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... | 0.055 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-6, 2), B=(1, -3), and C=(-8, 9). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordin... | 1.263 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-10, 8), B=(-8, 3), and C=(1, 6). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 1.958 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(5, 7), B=(-8, -4), and C=(6, -8), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | (2.049, -3.330) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-3, -5), B=(-6, -5), and C=(0, -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, coo... | (0.000, -9.500) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(4, 5), B=(-5, -5), and C=(-1, 2). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or radius... | 0.841 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-5, -7), B=(-4, 2), and C=(-6, -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... | (7.500, -9.500) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(4, -3), B=(-7, -7), and C=(-2, 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, coor... | (-2.632, 1.737) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(5, 4), B=(-7, -5), and C=(4, -6), find the measure (in degrees) of angle ABC. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coord... | 42.06° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, -10), B=(-10, -2), and C=(10, -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, ... | 69.44° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, -2), B=(6, 3), and C=(3, -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, coord... | 42.40° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(10, 7), B=(-8, 1), and C=(-3, 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, ... | (-76.000, 222.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-8, -2), B=(-4, -10), 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, coor... | 2.596 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(1, -6), B=(-2, -1), and C=(0, 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, coordin... | 0.919 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-1, -10), 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,... | (-27.667, 16.667) | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(9, 3), B=(-6, 5), 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, c... | (4.676, -0.931) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(3, -4), B=(-5, -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, ... | 84.09° | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-7, 9), B=(-10, -7), and C=(-1, 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, co... | 17.28° | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(-7, -6), B=(4, 7), 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, coordi... | 1.577 | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-4, -8), B=(-7, 10), and C=(-6, -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, c... | (10.286, -7.286) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 9), B=(-1, 8), and C=(7, 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... | 0.705 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-6, 3), B=(-10, 3), and C=(-6, 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,... | (-6.000, 3.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(7, 5), B=(2, 5), 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, coordin... | (-8.000, 35.000) | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(2, 7), B=(5, 7), and C=(-1, 4). Compute the radius of its incircle. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinat... | 0.645 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(0, 7), B=(10, -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, coord... | 39.81° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(6, -7), B=(-5, -4), and C=(0, 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, coord... | (-0.889, -1.259) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(6, 7), B=(-2, -3), 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, coord... | 7.05° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(3, 1), B=(3, -5), and C=(0, 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, co... | (33.333, 8.000) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, 5), B=(-10, -10), 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, co... | (4.545, -1.273) | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(6, 10), B=(0, 9), and C=(-3, -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... | 2.236 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-2, -3), B=(10, 0), and C=(7, 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... | 1.256 | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(-3, 9), B=(-7, 0), and C=(-8, 6), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (-11.545, 7.576) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(-6, 5), B=(10, 8), and C=(5, -1), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, o... | 50.33° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-8, -2), B=(-6, -7), and C=(1, 5), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | (-11.458, 0.017) | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-10, 10), B=(7, 4), and C=(0, -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, coor... | (3.066, 1.686) | Puzzle | advanced_geometry |
[
{
"content": "Given a triangle with vertices A=(5, 2), B=(3, 10), and C=(0, -2), determine the angle at B in degrees. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coordinates, or... | 28.07° | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(-7, 10), B=(3, 2), and C=(-1, 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... | 0.695 | Puzzle | advanced_geometry |
[
{
"content": "Consider triangle ABC with coordinates A=(9, 0), B=(9, -2), 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, coordina... | 0.924 | Puzzle | advanced_geometry |
[
{
"content": "Find the incircle radius of triangle ABC whose vertices are A=(1, -1), B=(10, 2), and C=(7, 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 ... | 2.332 | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(-1, 2), B=(-2, 2), and C=(-5, -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, coo... | 104.04° | Puzzle | advanced_geometry |
[
{
"content": "Given triangle ABC with coordinates A=(-6, 5), B=(9, -5), and C=(-3, -4), find the coordinates of its orthocenter. For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, coor... | (-7.286, -10.429) | Puzzle | advanced_geometry |
[
{
"content": "In triangle ABC with coordinates A=(4, -9), B=(-2, 9), 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, coor... | 29.74° | Puzzle | advanced_geometry |
[
{
"content": "For triangle with vertices A=(7, 1), B=(-5, -10), and C=(3, 7), determine the orthocenter (intersection of altitudes). For all geometry problems:\n1. Give coordinates in the form (x, y)\n2. Round decimal answers to 3 decimal places\n3. Use the degree symbol ° for angles\n4. Return only the angle, ... | (9.638, -0.241) | Puzzle | advanced_geometry |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.