messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
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[
{
"content": "ABCDEFGH is a regular octagon with center I and circumradius 3. Let S be the reflection of point B across point D. Let W be the reflection of point F across point S. Line P is the angle bisector of angle ACG. Point O is the reflection of point W across line P. Find the length of segment OG. Expres... | 16.68 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Z and circumradius 10. Point X is the reflection of point A across point E. Point N is the midpoint of segment ZD. Point H is the reflection of point X across segment NZ. Find the measure of angle NAH, in radians. Express your answer as a decimal number ... | 0.52 | MATH |
[
{
"content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 1. Point U is the reflection of point M across point E. Line T is the angle bisector of angle KMJ. Point Y is the reflection of point K across line T. Point O is the reflection of point F across point U. What is the distance be... | 5.75 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center G and circumradius 5. Line L is the perpendicular bisector of segment CG. Line Z passes through point E perpendicular to segment DC. Let N be the midpoint of segment DC. Line Q is the reflection of line L across line Z. Point R is the reflection of point N acro... | 11.61 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center H and circumradius 4. Let R be the midpoint of segment FA. Line O is the perpendicular bisector of segment RH. Point Y is the reflection of point C across point D. Point Q is the reflection of point F across line O. Find the distance between points Y and Q. ... | 5.29 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Z and circumradius 7. Let I be the midpoint of segment ZF. Point Q is the midpoint of segment CI. Point H is the reflection of point D across point F. What is the length of segment HQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nP... | 20.18 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center L and circumradius 5. Line O is the angle bisector of angle GJD. Point S is the reflection of point H across line O. Let W be the circumcircle of polygon ABCDEFGHIJ. Point K is the inversion of point S with respect to circle W. Point U is the reflecti... | 6.66 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center I and circumradius 3. Let N be the reflection of point E across point D. Line J passes through points I and A. Point G is the reflection of point N across line J. Line S is the angle bisector of angle BNG. Let R be the reflection of line J across line S.... | 5.81 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 6. Line X is the angle bisector of angle ECF. Let U be the circumcircle of polygon ABCDEF. Let V be the reflection of circle U across line X. Let P be the inversion of point A in circle V. Let R be the midpoint of segment DP. Find the leng... | 5.0 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center V and circumradius 10. Line N passes through points A and H. Point L is the reflection of point B across line N. Point Q is the midpoint of segment HL. Find the length of segment VQ. Express your answer as a decimal number rounded to 2 decimal places... | 6.95 | MATH |
[
{
"content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 4. Point V is the reflection of point B across point H. Let W be the reflection of point H across point G. Point N is the reflection of point V across segment LA. Find the distance between points N and W. Express your answer as... | 22.48 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center U and circumradius 6. Point P is the reflection of point B across point A. Point X is obtained by rotating point A by angle pi/6 about point G. Let W be the midpoint of segment XF. Point L is the midpoint of segment UW. Point V is the reflection of point L... | 8.15 | MATH |
[
{
"content": "Let ABCD be a square with center U and circumradius 1. Let H be the midpoint of segment UB. Let M be the reflection of point C across point A. Let K be the angle bisector of angle UMC. Point R is on line K with |RU| = 8. Line J passes through point H perpendicular to line K. Point W is obtained by... | 7.44 | MATH |
[
{
"content": "Let ABCDF be a regular 5-gon with center E and circumradius 11. Point J is the midpoint of segment EB. Let W be the perpendicular bisector of segment CA. Let P be the line through point A perpendicular to line W. Point I is the reflection of point J across line P. What is the distance between poin... | 9.7 | MATH |
[
{
"content": "ABDEFGH is a regular 7-gon with center C and circumradius 9. Let S be the perpendicular bisector of segment GC. Let M be the line through point A parallel to line S. Let Y be the reflection of line S across line M. Point O is the reflection of point A across line Y. Find the length of segment OH. ... | 20.69 | MATH |
[
{
"content": "Let ABCEFGHIJK be a regular 10-gon with center D and circumradius 8. Let T be the line through point G parallel to segment DK. Point V is the reflection of point B across line T. Let N be the midpoint of segment DK. Let O be the reflection of point N across point J. Find the length of segment OV. ... | 9.99 | MATH |
[
{
"content": "ABCDEGHI is a regular octagon with center F and circumradius 4. Let J be the midpoint of segment HI. Let K be the circumcircle of polygon ABCDEGHI. Point W is the inversion of point J with respect to circle K. Point V is the reflection of point W across point G. Find the distance between points V ... | 3.7 | MATH |
[
{
"content": "Let ABDE be a square with center C and circumradius 2. Let Z be the reflection of point B across point D. Let V be the angle bisector of angle ZBE. Line I passes through point E perpendicular to line V. Point N is the reflection of point Z across line I. What is the measure of angle ZNB, in radian... | 2.36 | MATH |
[
{
"content": "Let ACDEFG be a regular hexagon with center B and circumradius 9. Let J be the perpendicular bisector of segment CG. Let N be the line through point F parallel to line J. Point R is the midpoint of segment BA. Point H is the reflection of point R across line N. What is the measure of angle HCB, in... | 0.52 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 8. Point T is the midpoint of segment DG. Let N be the angle bisector of angle CGD. Point P is the reflection of point F across line N. Point H is the reflection of point G across point P. What is the distance between points H and T? E... | 9.07 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center L and circumradius 4. Let X be the perpendicular bisector of segment EB. Let U be the line through point C parallel to line X. Line V passes through point A perpendicular to line U. Point N is the reflection of point L across line V. What is the measure of a... | 2.09 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center K and circumradius 11. Point Q is obtained by rotating point F by angle pi/4 about point B. Let W be the angle bisector of angle BGK. Line O passes through point C parallel to line W. Line O and segment QD intersect at point J. Find the distance between po... | 17.3 | MATH |
[
{
"content": "ZN = 12. ABCD is a square with center N and circumradius 4. Let I be the reflection of point B across point D. Let L be the reflection of point A across point I. Let T be the circumcircle of polygon ABCD. Point O is the inversion of point L with respect to circle T. What is the length of segment L... | 23.67 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 3. Point T is the midpoint of segment HC. Segments BE and GD intersect at point Q. What is the length of segment TQ? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{... | 2.57 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center U and circumradius 10. Let V be the perpendicular bisector of segment BC. Let P be the midpoint of segment FE. Point R is the reflection of point P across line V. Find the distance between points B and R. Express your answer as a decimal number rounded ... | 14.86 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center R and circumradius 9. Line F passes through points E and R. Line T is the reflection of line F across point C. Point L is the reflection of point C across line T. Point U is the reflection of point L across segment BA. Find the distance between points U and A. ... | 26.42 | MATH |
[
{
"content": "ABDEFGHI is a regular octagon with center C and circumradius 12. Point Z is obtained by rotating point H by angle 11pi/12 about point G. Let S be the circumcircle of polygon ABDEFGHI. Let W be the perpendicular bisector of segment CB. Line K is the angle bisector of angle BEG. Let J be the reflect... | 8.98 | MATH |
[
{
"content": "ABCDFGHIJKLM is a regular dodecagon with center E and circumradius 10. Line Z is the perpendicular bisector of segment GI. Let X be the perpendicular bisector of segment FL. Let O be the line through point I parallel to line Z. Line P is the reflection of line X across line O. Let U be the reflect... | 9.73 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center P and circumradius 6. Let X be the midpoint of segment EC. Line Q is the angle bisector of angle FXC. Point V is the reflection of point E across line Q. Let S be the midpoint of segment VP. Find the distance between points S and D. Express your answer as a ... | 3.05 | MATH |
[
{
"content": "ABCDEG is a regular hexagon with center F and circumradius 7. Line M passes through points G and A. Let Z be the circumcircle of polygon ABCDEG. Circle O is the reflection of circle Z across line M. Let S be the inversion of point D in circle O. What is the distance between points C and S? Express... | 16.09 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center O and circumradius 8. Line M passes through points O and D. Line K is the reflection of line M across point C. Let Z be the line through point C perpendicular to line K. Point U is on line Z. What is the measure of angle UEB, in radians? Express your answer a... | 0.45 | MATH |
[
{
"content": "ABCDEFGIJK is a regular 10-gon with center H and circumradius 9. Let P be the vector from point I to point D. Point Z is the translation of point F by vector P. Point L is obtained by rotating point H by angle 2pi/3 about point Z. Point Y is the translation of point A by vector P. Line M passes th... | 16.08 | MATH |
[
{
"content": "BCDEF is a regular 5-gon with center A and circumradius 12. Let Z be the rotation of point C by angle 3pi/4 around point F. Line S is the perpendicular bisector of segment ED. Let R be the line through point Z perpendicular to segment BC. Let G be the reflection of line R across line S. Point W is... | 29.79 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center N and circumradius 12. Let Z be the line through points E and D. Let K be the midpoint of segment NA. Let Y be the reflection of point E across point A. Let G be the reflection of line Z through point K. Line V passes through points C and Y. Let I be the li... | 16.9 | MATH |
[
{
"content": "Let ABCDFGHIJ be a regular 9-gon with center E and circumradius 6. Let P be the angle bisector of angle GAC. Let R be the circumcircle of polygon ABCDFGHIJ. Circle K is the reflection of circle R across line P. Let Z be the inversion of point C in circle K. Let N be the inversion of point Z in cir... | 7.48 | MATH |
[
{
"content": "Let ABDEFG be a regular hexagon with center C and circumradius 8. Point V is the reflection of point E across point A. Point R is the midpoint of segment CD. Let M be the line through points R and V. Point O is the reflection of point B across line M. What is the distance between points V and O? E... | 21.17 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center W and circumradius 1. Let V be the line through points E and L. Line R passes through point G perpendicular to line V. Let Q be the midpoint of segment GF. Line Y is the reflection of line R across point J. Point N is the reflection of point J across... | 4.38 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center W and circumradius 7. Point M is the midpoint of segment JG. Point P is the reflection of point E across point H. Point R is the reflection of point B across segment DP. What is the length of segment MR? Express your answer as a decimal number rounded to ... | 10.83 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center X and circumradius 7. Line W is the angle bisector of angle JGI. Line N is the reflection of line W across point C. Let Y be the reflection of point K across point I. Point S is the reflection of point A across line N. Point M is the reflection o... | 81.67 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center U and circumradius 11. Line Q is the angle bisector of angle IGU. Point R is the reflection of point U across line Q. Let O be the circumcircle of polygon ABCDEFGHIJK. Circle S is the reflection of circle O across point H. Let Z be the inversion of point... | 9.75 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center P and circumradius 10. Let J be the circumcircle of polygon ABCDEFGH. Let K be the line through points C and D. Let R be the angle bisector of angle CHF. Let Z be the line through points F and H. Lines K and Z intersect at point M. Circle O is the refl... | 27.06 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center J and circumradius 3. Point Z is the reflection of point G across point E. Line I is the perpendicular bisector of segment JG. Line S passes through point Z parallel to line I. Point T is the reflection of point D across line S. What is the distance betwee... | 4.42 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center S and circumradius 4. Line P passes through points A and D. Let Z be the line through point F parallel to line P. Point L is the reflection of point G across line Z. Let W be the midpoint of segment KS. Find the length of segment WL. Express your answer ... | 4.15 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center X and circumradius 7. Let Z be the angle bisector of angle BAE. Let L be the rotation of point E by angle 3pi/4 around point B. Line T is the reflection of line Z across point L. Point W is the reflection of point B across line T. Point O is the reflection of p... | 104.55 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 2. Let P be the circumcircle of polygon ABCDEG. Let V be the reflection of circle P through point C. Point O is the inversion of point A with respect to circle V. Let I be the midpoint of segment DO. Find the distance between points I ... | 4.21 | MATH |
[
{
"content": "ABCDEFHIJKLM is a regular dodecagon with center G and circumradius 9. Let R be the reflection of point K across point J. Let T be the angle bisector of angle AJR. Point P is the reflection of point B across line T. Let W be the line through points D and H. Line S passes through point F parallel to... | 16.79 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center I and circumradius 7. Point M is obtained by rotating point E by angle 5pi/12 about point B. Line W is the angle bisector of angle ICM. Point P is the reflection of point M across line W. Point K is the midpoint of segment EB. Point F is the midpoint of segment... | 11.16 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center S and circumradius 11. Line M passes through points J and C. Let L be the line through point I parallel to line M. Let W be the reflection of line L across line M. Point U is the reflection of point J across line W. What is the length of segment IU? Expre... | 19.51 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Q and circumradius 1. Point P is obtained by rotating point A by angle pi about point E. Point I is the reflection of point E across segment BP. Line X passes through point H perpendicular to segment BP. Point V is the reflection of point I across line... | 1.33 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center Y and circumradius 12. Let J be the circumcircle of polygon ABCDEFGHI. Let S be the reflection of point E across point F. Let V be the reflection of circle J through point S. Point R is the inversion of point I with respect to circle V. Let N be the inversi... | 1.18 | MATH |
[
{
"content": "Let ABCDF be a regular 5-gon with center E and circumradius 1. Line N passes through points D and F. Let R be the line through point A parallel to line N. Let Q be the perpendicular bisector of segment CB. Let H be the reflection of line R across line Q. Let J be the circumcircle of polygon ABCDF.... | 2.44 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center W and circumradius 5. Let Y be the angle bisector of angle CED. Let P be the line through points B and E. Point S is the reflection of point D across line P. Line I is the reflection of line Y across point C. Point R is the reflection of point B across line I. ... | 7.51 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center M and circumradius 9. Point Q is the reflection of point F across point M. Let L be the perpendicular bisector of segment QI. Let S be the reflection of point Q across point I. Let N be the midpoint of segment AF. Point Z is the reflection of point N ac... | 16.64 | MATH |
[
{
"content": "Let ABCDEFHI be a regular octagon with center G and circumradius 6. Let M be the reflection of point A across point E. Let Y be the line through point M perpendicular to segment AI. Point T is the reflection of point C across line Y. Point L is the reflection of point F across segment DH. Find the... | 18.93 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center V and circumradius 9. Let K be the line through points E and H. Let P be the line through point D parallel to segment BF. Lines K and P intersect at point R. What is the length of segment RV? Express your answer as a decimal number rounded to 2 decimal pla... | 11.69 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center X and circumradius 1. Let O be the circumcircle of polygon ABCDEFGHI. Point Q is the reflection of point D across point H. Point P is the reflection of point I across point Q. Let M be the reflection of circle O through point Q. Point K is the inversion... | 0.85 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center U and circumradius 7. Point K is the midpoint of segment FE. Point Q is the reflection of point K across point B. Point Z is the midpoint of segment JQ. Let M be the reflection of point Z across point E. What is the length of segment BM? Express your ... | 28.82 | MATH |
[
{
"content": "ABCD is a square with center T and circumradius 3. Point Y is the midpoint of segment AB. Let R be the circumcircle of polygon ABCD. Let N be the inversion of point Y in circle R. Let Q be the midpoint of segment AN. What is the distance between points Q and A? Express your answer as a decimal num... | 1.5 | MATH |
[
{
"content": "Let ABCD be a square with center E and circumradius 10. Let V be the circumcircle of polygon ABCD. Point K is obtained by rotating point E by angle 3pi/4 about point D. Line L passes through points E and K. Point I is the reflection of point C across line L. Point H is the midpoint of segment AK. ... | 4.15 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center S and circumradius 2. Let V be the perpendicular bisector of segment SE. Point Z is the reflection of point G across line V. Let X be the line through points B and F. Line O passes through points H and C. Point W is the intersection of lines X and O. Line ... | 7.78 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center T and circumradius 4. Point U is obtained by rotating point C by angle 7pi/12 about point G. Point P is obtained by rotating point H by angle 11pi/12 about point T. Let V be the line through points U and B. Point X is the reflection of point H across l... | 11.0 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Z and circumradius 3. Line V passes through points Z and G. Line M passes through point L parallel to line V. Let W be the reflection of line M across line V. Point X is the reflection of point A across line W. Let T be the midpoint of segment GX. Wh... | 3.97 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Z and circumradius 3. Let Q be the perpendicular bisector of segment GL. Let R be the line through point H parallel to line Q. Point S is the reflection of point D across line R. Point W is the reflection of point S across line Q. Find the length... | 5.2 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center R and circumradius 3. Line N is the perpendicular bisector of segment BR. Let U be the midpoint of segment AF. Let Y be the reflection of point E across point C. Point V is the reflection of point Y across line N. Point P is the reflection of point V acr... | 9.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 10. Point V is the reflection of point E across point B. Let N be the perpendicular bisector of segment EC. Point P is the reflection of point E across point A. Let M be the line through point V perpendicular to line N. Let K be the li... | 32.45 | MATH |
[
{
"content": "Let ABCD be a square with center J and circumradius 1. Let P be the circumcircle of polygon ABCD. Let S be the midpoint of segment BJ. Point M is the midpoint of segment SA. Let T be the inversion of point M in circle P. What is the length of segment MT? Express your answer as a decimal number rou... | 1.23 | MATH |
[
{
"content": "Let BCDEFGHIJK be a regular 10-gon with center A and circumradius 5. Let N be the line through points D and B. Line M is the reflection of line N across point K. Point V is the reflection of point F across line M. Line P passes through points V and E. Point L is the intersection of lines P and N. ... | 8.29 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center T and circumradius 11. Point M is the reflection of point B across point A. Let N be the reflection of point D across point A. Let Y be the circumcircle of polygon ABCDEF. Point X is the inversion of point N with respect to circle Y. What is the measure of a... | 2.09 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 9. Let N be the vector from point F to point B. Point Z is the translation of point C by vector N. Line V is the perpendicular bisector of segment FE. Line Q is the reflection of line V across point Z. Point U is the reflection of poin... | 35.72 | MATH |
[
{
"content": "Let ABCDEFGHIKLM be a regular dodecagon with center J and circumradius 2. Let Y be the angle bisector of angle ABD. Point Z is the midpoint of segment JI. Line P is the reflection of line Y across point M. Point V is the reflection of point J across line P. What is the length of segment ZV? Expres... | 6.55 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 2. Point S is the reflection of point E across point D. Point W is the reflection of point D across segment CS. Point L is the midpoint of segment AW. What is the distance between points B and L? Express your answer as a decimal number... | 1.0 | MATH |
[
{
"content": "ACDEFGHIJKL is a regular 11-gon with center B and circumradius 3. Let Q be the vector from point G to point C. Line R is the angle bisector of angle ICK. Let Y be point I translated by vector Q. Let S be the perpendicular bisector of segment CD. Line O passes through point A perpendicular to line ... | 5.56 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 12. Let N be the circumcircle of polygon ABCDEF. Line Q is the angle bisector of angle BCD. Let Y be the midpoint of segment AC. Let K be the line through point F perpendicular to line Q. Let Z be the inversion of point Y in circle N. Poin... | 48.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center K and circumradius 1. Line O is the angle bisector of angle EBA. Let I be the perpendicular bisector of segment DE. Let Q be the reflection of line I across line O. Point J is the reflection of point F across line Q. Find the distance between points J an... | 1.0 | MATH |
[
{
"content": "ABCDEFGHJKLM is a regular dodecagon with center I and circumradius 10. Line S passes through points E and L. Point T is the reflection of point K across point E. Point P is the reflection of point T across line S. Point Y is the midpoint of segment IP. What is the length of segment KY? Express you... | 23.13 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Q and circumradius 11. Let X be the circumcircle of polygon ABCDEFGH. Point V is the midpoint of segment HC. Let T be the inversion of point V in circle X. Let Z be the midpoint of segment TH. What is the distance between points A and Z? Express your answe... | 6.37 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center L and circumradius 11. Line R is the angle bisector of angle GHB. Point P is the reflection of point G across line R. Let V be the midpoint of segment PD. Let Y be the midpoint of segment PH. What is the length of segment VY? Express your answer as a decim... | 11.0 | MATH |
[
{
"content": "ACDEFGHIJKLM is a regular dodecagon with center B and circumradius 12. Line T passes through point D perpendicular to segment AJ. Let W be the line through point E perpendicular to line T. Point P is the reflection of point F across line W. Find the distance between points F and P. Express your an... | 3.22 | MATH |
[
{
"content": "Let ABDEFGHIJKLM be a regular dodecagon with center C and circumradius 9. Let W be the circumcircle of polygon ABDEFGHIJKLM. Circle N is the reflection of circle W across point H. Point O is the inversion of point I with respect to circle N. Line X passes through points K and D. Point Y is the ref... | 20.54 | MATH |
[
{
"content": "ABCDFGHI is a regular octagon with center E and circumradius 4. Let X be the perpendicular bisector of segment DF. Line T passes through point F parallel to line X. Let R be the line through point H perpendicular to line T. Line O is the perpendicular bisector of segment EG. Line S is the reflecti... | 3.67 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Q and circumradius 4. Line I is the angle bisector of angle GEA. Line O is the reflection of line I across point B. Point Y is the reflection of point G across point E. Let Z be the line through point E perpendicular to line O. Point J is the reflectio... | 5.3 | MATH |
[
{
"content": "ABCDEFGHIJKM is a regular dodecagon with center L and circumradius 8. Let Y be the rotation of point C by angle 5pi/12 around point D. Let O be the perpendicular bisector of segment IF. Line V passes through point G parallel to line O. Point S is the intersection of line V and segment EJ. What is ... | 11.12 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center W and circumradius 4. Let R be the circumcircle of polygon ABCDEFGH. Circle Z is the reflection of circle R across point F. Let Q be the reflection of circle Z through point W. Point L is the inversion of point H with respect to circle Q. What is the lengt... | 9.45 | MATH |
[
{
"content": "ABDEFG is a regular hexagon with center C and circumradius 5. Let W be the line through points F and C. Let N be the reflection of point E across point B. Let Z be the midpoint of segment AN. Let S be the line through point Z perpendicular to segment BD. Line V is the reflection of line S across l... | 4.59 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Z and circumradius 6. Line N is the perpendicular bisector of segment BC. Line R passes through point Z perpendicular to line N. Line T passes through point C parallel to line R. Point W is the reflection of point B across point C. Point X is the... | 7.94 | MATH |
[
{
"content": "Let ABCDEFH be a regular 7-gon with center G and circumradius 4. Point L is the midpoint of segment GH. Point Z is the midpoint of segment BC. Point T is the reflection of point C across segment EZ. Let I be the midpoint of segment LT. Find the length of segment FI. Express your answer as a decima... | 4.66 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 4. Point O is the reflection of point D across segment BK. Let T be the perpendicular bisector of segment JK. Line Z passes through point L parallel to line T. Point U is the intersection of line Z and segment BK. Let Q be the ... | 2.48 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Z and circumradius 8. Let V be the perpendicular bisector of segment FD. Line O passes through point D parallel to line V. Point J is the reflection of point Z across line O. Let R be the midpoint of segment CB. Point I is the reflection of point R across po... | 4.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center T and circumradius 3. Point H is the midpoint of segment DC. Let Q be the circumcircle of polygon ABCDEF. Circle W is the reflection of circle Q across point B. Let X be the inversion of point H in circle W. Find the distance between points X and H. Expr... | 5.16 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center U and circumradius 6. Let P be the midpoint of segment AU. Let H be the reflection of point P across point A. Let I be the midpoint of segment DP. What is the distance between points H and I? Express your answer as a decimal number rounded to 2 decimal p... | 10.5 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 12. Line Z passes through points X and B. Line T passes through point C perpendicular to line Z. Let I be the midpoint of segment FD. Point W is the reflection of point E across line T. Find the distance between points W and I. Expre... | 31.55 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center V and circumradius 3. Let N be the reflection of point A across point F. Let U be the perpendicular bisector of segment AF. Line Q is the reflection of line U across point C. Let K be the line through point N perpendicular to line Q. Let H be the reflection ... | 1.05 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 3. Let W be the circumcircle of polygon ABCDEF. Let R be the reflection of circle W through point F. Point O is the inversion of point B with respect to circle R. Line U is the angle bisector of angle CBO. Let L be the reflection of circle... | 4.17 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center Q and circumradius 9. Let R be the angle bisector of angle HCA. Point W is the midpoint of segment DA. Line S passes through point F perpendicular to line R. Point N is the reflection of point W across line S. Point O is the reflection of point A across ... | 7.47 | MATH |
[
{
"content": "ABCDEGHIJKLM is a regular dodecagon with center F and circumradius 1. Point Y is the midpoint of segment HL. Let Z be the line through point Y perpendicular to segment EM. Point U is the reflection of point B across line Z. Let O be the perpendicular bisector of segment MB. Line R passes through p... | 2.19 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center G and circumradius 4. Line S is the perpendicular bisector of segment AG. Let O be the circumcircle of polygon ABCDEF. Let X be the reflection of circle O across line S. Point L is the inversion of point D with respect to circle X. Find the distance between ... | 2.0 | MATH |
[
{
"content": "Let ABCDEFGHJ be a regular 9-gon with center I and circumradius 2. Point S is obtained by rotating point C by angle pi about point H. Let L be the circumcircle of polygon ABCDEFGHJ. Let V be the midpoint of segment HA. Line Y passes through points J and S. Point X is the reflection of point V acro... | 3.71 | MATH |
[
{
"content": "Let ABCDEFGI be a regular octagon with center H and circumradius 12. Line Z is the angle bisector of angle ECD. Line N is the reflection of line Z across point I. Point Y is obtained by rotating point F by angle pi about point C. Let X be the midpoint of segment IA. Let W be the reflection of line... | 250.4 | MATH |
[
{
"content": "ABCDEGHI is a regular octagon with center F and circumradius 8. Let X be the reflection of point E across point I. Let O be the midpoint of segment IH. Point P is obtained by rotating point F by angle 11pi/12 about point I. Line W passes through points H and G. Let U be the midpoint of segment IX.... | 12.19 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center M and circumradius 1. Let V be the midpoint of segment IE. Line L passes through point J parallel to segment IE. Line T is the perpendicular bisector of segment DC. Line N is the reflection of line L across point E. Let W be the reflection of line T throu... | 2.17 | MATH |
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