messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
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[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center R and circumradius 3. Let W be the reflection of point K across point G. Line Y passes through points C and A. Let S be the reflection of point A across point W. Line L passes through point I perpendicular to line Y. Let Z be the circumcircle of poly... | 4.27 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center U and circumradius 9. Let N be the reflection of point U across point C. Let J be the reflection of point U across point A. Let W be the midpoint of segment NB. What is the distance between points W and J? Express your answer as a decimal number rounded to 2... | 23.38 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center S and circumradius 5. Let R be the angle bisector of angle AEF. Point X is the reflection of point C across line R. Let U be the circumcircle of polygon ABCDEF. Let O be the inversion of point X in circle U. Find the length of segment AO. Express your an... | 5.12 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 5. Point K is the midpoint of segment AY. Line O is the angle bisector of angle FGD. Let Q be the midpoint of segment BE. Let R be the reflection of line O through point D. Point T is the reflection of point K across line R. Let V be... | 9.68 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Q and circumradius 8. Let F be the perpendicular bisector of segment CB. Let L be the line through point B perpendicular to line F. Let O be the midpoint of segment BQ. Point Z is the reflection of point O across line L. Find the distance between points B a... | 4.0 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center K and circumradius 6. Let U be the circumcircle of polygon ABCDEFGHIJ. Let S be the reflection of point A across point H. Circle N is the reflection of circle U across point I. Let T be the inversion of point S in circle N. Find the length of segment KT. ... | 11.46 | MATH |
[
{
"content": "Let ABCDFGHI be a regular octagon with center E and circumradius 5. Let T be the midpoint of segment GF. Point Q is the midpoint of segment TE. Point P is the midpoint of segment TF. Find the measure of angle QPF, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\n... | 1.96 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center U and circumradius 7. Let P be the perpendicular bisector of segment EA. Let O be the line through points C and A. Line K is the reflection of line P across line O. Point S is the midpoint of segment AC. Point L is the reflection of point A across line K. L... | 39.35 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center I and circumradius 9. Let R be the circumcircle of polygon ABCDEF. Line Z is the angle bisector of angle BFD. Point X is obtained by rotating point B by angle pi/4 about point E. Let Y be the reflection of circle R through point B. Point W is the inversi... | 44.61 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center M and circumradius 12. Let T be the midpoint of segment AC. Let Z be the midpoint of segment BT. Let P be the reflection of point Z across point F. What is the distance between points B and P? Express your answer as a decimal number rounded to 2 decimal plac... | 39.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center O and circumradius 9. Let U be the reflection of point B across point A. Line Z is the perpendicular bisector of segment UA. Point S is the reflection of point D across line Z. Point V is the midpoint of segment UO. Point Q is the reflection of point V a... | 47.41 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center N and circumradius 2. Point Q is obtained by rotating point C by angle 7pi/12 about point E. Point X is the midpoint of segment BF. Let L be the midpoint of segment XG. Line O is the angle bisector of angle QNF. Point R is the reflection of point L across l... | 1.98 | MATH |
[
{
"content": "ABDEFGHIJKL is a regular 11-gon with center C and circumradius 3. Let Z be the circumcircle of polygon ABDEFGHIJKL. Line N is the angle bisector of angle GBL. Line Y is the perpendicular bisector of segment HF. Let V be the reflection of line N across line Y. Let X be the reflection of circle Z ac... | 4.22 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center T and circumradius 10. Line N passes through point F parallel to segment GI. Line U passes through point C parallel to line N. Point Q is the reflection of point B across line U. Find the length of segment QI. Express your answer as a decimal number round... | 20.0 | MATH |
[
{
"content": "ABCDEGHIJK is a regular 10-gon with center F and circumradius 5. Point R is the midpoint of segment AH. Let T be the circumcircle of polygon ABCDEGHIJK. Circle O is the reflection of circle T across point I. Point Q is the midpoint of segment CR. Point V is the inversion of point Q with respect to... | 7.84 | MATH |
[
{
"content": "ACDEFG is a regular hexagon with center B and circumradius 10. Line L is the perpendicular bisector of segment DB. Point W is the reflection of point D across segment GA. Let O be the angle bisector of angle GBF. Let K be the line through point W parallel to line O. Line N is the reflection of lin... | 86.75 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center S and circumradius 9. Let Y be the reflection of point F across point B. Let X be the perpendicular bisector of segment EY. Line J passes through point E parallel to line X. Point H is the reflection of point A across line J. What is the distance between poi... | 22.47 | MATH |
[
{
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 9. Let Z be the angle bisector of angle DMC. Point X is the midpoint of segment FM. Point Y is the reflection of point G across line Z. Point T is the reflection of point H across point X. Find the distance between points Y and T. ... | 13.26 | MATH |
[
{
"content": "BCDEFGHIJKLM is a regular dodecagon with center A and circumradius 8. Point P is the reflection of point I across point B. Point N is obtained by rotating point L by angle 3pi/4 about point K. Line Z is the angle bisector of angle ACP. Let S be the line through point N parallel to line Z. Point Q ... | 17.47 | MATH |
[
{
"content": "ABDEFGHIJKLM is a regular dodecagon with center C and circumradius 6. Point N is obtained by rotating point F by angle 3pi/4 about point K. Let X be the circumcircle of polygon ABDEFGHIJKLM. Let V be the angle bisector of angle NDI. Let T be the reflection of circle X across line V. Let Y be the i... | 9.29 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center V and circumradius 9. Let W be the perpendicular bisector of segment VA. Let N be the reflection of line W through point A. Point R is the reflection of point E across line N. What is the distance between points A and R? Express your answer as a decimal numb... | 23.81 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center N and circumradius 9. Line T passes through points A and B. Let G be the reflection of line T through point E. Line Z passes through point A perpendicular to line G. Point L is the reflection of point D across line Z. What is the length of segment AL? Expre... | 17.12 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center J and circumradius 2. Let K be the circumcircle of polygon ABCDEF. Let T be the reflection of point E across point C. Let Z be the line through points D and T. Let Q be the reflection of circle K through point C. Let P be the reflection of circle Q across li... | 4.58 | MATH |
[
{
"content": "Let ABCDEFHIJKLM be a regular dodecagon with center G and circumradius 1. Let W be the midpoint of segment IA. Point Q is the midpoint of segment LM. Let N be the midpoint of segment EQ. Find the length of segment NW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent ... | 0.34 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center U and circumradius 12. Point X is the reflection of point D across point H. Line W passes through points J and X. Let S be the perpendicular bisector of segment GH. Let R be the reflection of line W across line S. Point Z is the reflection of poi... | 8.78 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 3. Let H be the perpendicular bisector of segment KA. Point Q is the reflection of point D across line H. Let U be the reflection of point A across point E. Let R be the midpoint of segment EU. Find the distance between points R and Q. Exp... | 10.5 | MATH |
[
{
"content": "Let BCDEFGHIJKLM be a regular dodecagon with center A and circumradius 9. Point Y is obtained by rotating point B by angle pi/6 about point J. Line O is the angle bisector of angle JIK. Point U is the reflection of point H across line O. Let N be the angle bisector of angle GAU. Point V is the ref... | 14.17 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center W and circumradius 4. Let Y be the angle bisector of angle WCD. Point S is the reflection of point F across line Y. Line T passes through points D and F. Point N is the reflection of point S across segment BC. Point P is the reflection of point B across line... | 17.44 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Q and circumradius 11. Line Z is the perpendicular bisector of segment DA. Let M be the line through point A parallel to line Z. Let O be the line through point D parallel to line M. Point R is the reflection of point B across line O. Point X is the midpoi... | 10.16 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center Q and circumradius 8. Let N be the midpoint of segment HD. Let Y be the perpendicular bisector of segment NK. Point Z is the reflection of point A across line Y. Point O is the reflection of point Z across point D. What is the length of segment OZ? Expre... | 7.2 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center V and circumradius 9. Point P is the reflection of point A across point E. Point N is the reflection of point C across point E. Line U passes through points A and N. Point S is the reflection of point P across line U. Point K is the midpoint of segment BD... | 36.26 | MATH |
[
{
"content": "Let ABCD be a square with center J and circumradius 4. Let Q be the circumcircle of polygon ABCD. Line V is the angle bisector of angle DCJ. Point U is obtained by rotating point D by angle 3pi/4 about point J. Let N be the rotation of point C by angle 11pi/12 around point A. Point G is the reflec... | 1.18 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center W and circumradius 8. Let O be the perpendicular bisector of segment BW. Let V be the line through point E perpendicular to line O. Let L be the reflection of point F across point E. Let G be the reflection of point F across point A. Line X is the angle ... | 8.0 | MATH |
[
{
"content": "Let ABCDF be a regular 5-gon with center E and circumradius 4. Line P passes through points F and E. Line S is the reflection of line P across point B. Line X passes through points B and C. Point Q is the intersection of lines X and S. Find the distance between points A and Q. Express your answer ... | 4.56 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center O and circumradius 9. Line M is the angle bisector of angle DBG. Point V is the reflection of point A across line M. Point W is the midpoint of segment CH. What is the length of segment VW? Express your answer as a decimal number rounded to 2 dec... | 13.64 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center N and circumradius 4. Let U be the rotation of point N by angle pi/2 around point D. Line L is the perpendicular bisector of segment UN. Line J passes through point E perpendicular to line L. Let V be the perpendicular bisector of segment CD. Line P is t... | 2.62 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center M and circumradius 4. Let X be the line through point M parallel to segment EB. Point U is the midpoint of segment EB. Point I is the midpoint of segment UE. Point G is the reflection of point I across line X. What is the length of segment GB? Express your ... | 6.22 | MATH |
[
{
"content": "Let ABCDEGHI be a regular octagon with center F and circumradius 4. Let X be the reflection of point E across point B. Let Q be the circumcircle of polygon ABCDEGHI. Let V be the angle bisector of angle CFX. Line R passes through point X perpendicular to line V. Let P be the midpoint of segment FG... | 30.88 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Y and circumradius 2. Point X is the reflection of point B across segment FA. Let P be the angle bisector of angle YCI. Line T is the reflection of line P across point F. Let R be the reflection of point D across point H. Line Q passes through point ... | 1.83 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center R and circumradius 11. Let I be the angle bisector of angle GEA. Point Q is the reflection of point G across line I. Let W be the line through point E perpendicular to line I. Point K is the reflection of point Q across line W. What is the length of segment K... | 17.72 | MATH |
[
{
"content": "ABCEFG is a regular hexagon with center D and circumradius 12. Line U passes through points G and A. Let L be the line through point C parallel to segment EA. Point M is the intersection of lines L and U. Point Q is the reflection of point D across point F. Find the distance between points Q and M... | 43.27 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 2. Let R be the line through points B and K. Line N is the reflection of line R across point D. Let T be the circumcircle of polygon ABCDEF. Let S be the reflection of line N through point K. Let J be the reflection of circle T across line... | 1.5 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center Y and circumradius 5. Point S is obtained by rotating point G by angle 5pi/12 about point D. Point T is the intersection of segments FS and JC. Let U be the midpoint of segment TB. Let W be the circumcircle of polygon ABCDEFGHIJ. Let V be the inversion of... | 11.4 | MATH |
[
{
"content": "Let ABCDEFGHIJLM be a regular dodecagon with center K and circumradius 11. Let Y be the circumcircle of polygon ABCDEFGHIJLM. Point V is the reflection of point B across segment MG. Let O be the midpoint of segment KA. Point P is the inversion of point V with respect to circle Y. What is the dista... | 8.28 | MATH |
[
{
"content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 9. Let Q be the line through points J and F. Point Y is the reflection of point I across line Q. Let W be the midpoint of segment LY. Let R be the midpoint of segment MW. What is the length of segment ER? Express your answer as... | 15.08 | MATH |
[
{
"content": "ABCEFGHIJKL is a regular 11-gon with center D and circumradius 11. Let S be the circumcircle of polygon ABCEFGHIJKL. Let U be the reflection of circle S through point L. Let W be the perpendicular bisector of segment EF. Circle O is the reflection of circle U across line W. Point Z is the inversio... | 25.66 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center M and circumradius 11. Let J be the reflection of point F across point D. Point V is the midpoint of segment CE. Let P be the reflection of point J across point V. What is the distance between points F and P? Express your answer as a decimal number rounded t... | 11.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 9. Line T is the perpendicular bisector of segment DL. Let N be the perpendicular bisector of segment CB. Let S be the reflection of line N across line T. Point X is the reflection of point F across line S. What is the measure of angle... | 2.62 | MATH |
[
{
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 4. Let T be the reflection of point F across point K. Point N is the midpoint of segment TM. Point Y is the reflection of point N across segment BL. Find the distance between points Y and A. Express your answer as a decimal number ... | 7.3 | MATH |
[
{
"content": "Let CK = 5. ABDEFGHIJLMN is a regular dodecagon with center K and circumradius 10. Let X be the line through points J and I. Line S is the reflection of line X across point M. Let Q be the reflection of line S through point K. Point V is the intersection of segment JG and line Q. What is the lengt... | 11.57 | MATH |
[
{
"content": "ABCDEFGIJ is a regular 9-gon with center H and circumradius 9. Line S is the angle bisector of angle DJC. Point X is the reflection of point D across line S. Let V be the midpoint of segment GB. Point Z is the midpoint of segment XV. Find the length of segment ZJ. Express your answer as a decimal ... | 12.23 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 10. Point T is the reflection of point D across point B. Line Y passes through point T parallel to segment AD. Point R is the reflection of point E across line Y. What is the length of segment CR? Express your answer as a decimal numbe... | 34.64 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center N and circumradius 3. Line Q passes through points E and H. Line K passes through point G parallel to segment AH. Point S is the intersection of lines K and Q. Find the length of segment SA. Express your answer as a decimal number rounded to 2 decimal plac... | 2.81 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center T and circumradius 9. Let Z be the midpoint of segment AC. Segments HC and BF intersect at point Y. Find the length of segment ZY. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format: \\boxed{You... | 5.58 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center S and circumradius 11. Let M be the midpoint of segment EF. Point L is the reflection of point M across point C. Point R is the reflection of point B across segment EF. Find the length of segment LR. Express your answer as a decimal number rounded to 2 d... | 59.49 | MATH |
[
{
"content": "ABCDEG is a regular hexagon with center F and circumradius 3. Let M be the circumcircle of polygon ABCDEG. Line R is the angle bisector of angle DCG. Point K is on line R. Let J be the inversion of point K in circle M. What is the distance between points D and J? Express your answer as a decimal n... | 3.0 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Q and circumradius 1. Let S be the circumcircle of polygon ABCDEFGH. Line W passes through points D and B. Circle O is the reflection of circle S across line W. Let L be the inversion of point F in circle O. What is the length of segment LB? Express your a... | 0.89 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center X and circumradius 12. Let Z be the line through point C parallel to segment AK. Let P be the midpoint of segment AK. Let O be the midpoint of segment LD. Point V is the reflection of point P across line Z. Point Y is the reflection of point V ac... | 30.23 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center V and circumradius 10. Let W be the line through points B and C. Point Q is the reflection of point G across line W. Point X is the reflection of point F across segment BD. What is the distance between points Q and X? Express your answer as a decimal numbe... | 21.41 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center M and circumradius 9. Let P be the circumcircle of polygon ABCDEF. Let V be the midpoint of segment ED. Let S be the reflection of circle P through point B. Line I is the perpendicular bisector of segment BV. Circle X is the reflection of circle S across poi... | 28.85 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center T and circumradius 10. Line U is the perpendicular bisector of segment GF. Let Q be the reflection of point D across point G. Let S be the midpoint of segment FC. Point L is the reflection of point S across line U. What is the distance between points Q... | 25.85 | MATH |
[
{
"content": "Let BCDEFGH be a regular 7-gon with center A and circumradius 7. Let I be the line through points D and E. Line O passes through point G parallel to line I. Point Z is the reflection of point C across line O. Let P be the rotation of point C by angle 2pi/3 around point G. Line N is the reflection ... | 1015.68 | MATH |
[
{
"content": "ABCDEGH is a regular 7-gon with center F and circumradius 6. Line Y passes through points D and G. Let R be the line through points F and C. Point O is the intersection of lines R and Y. Let P be the reflection of point E across point A. Find the distance between points P and O. Express your answe... | 23.4 | MATH |
[
{
"content": "ABCDEG is a regular hexagon with center F and circumradius 5. Let W be the line through points E and C. Point N is the reflection of point E across point C. Line R passes through point B perpendicular to line W. Let H be the line through point F perpendicular to line R. Point U is the reflection o... | 8.66 | MATH |
[
{
"content": "Let ABCE be a square with center D and circumradius 3. Line X is the perpendicular bisector of segment DC. Let Q be the line through point D parallel to line X. Let P be the reflection of line Q across line X. Let T be the reflection of line X across line P. Point K is the reflection of point A ac... | 12.37 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center U and circumradius 6. Let Y be the rotation of point E by angle 5pi/6 around point F. Point T is the midpoint of segment YU. Let J be the midpoint of segment BT. Point M is the midpoint of segment JT. Point O is the midpoint of segment FE. Find the dista... | 5.13 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center N and circumradius 8. Point K is the reflection of point E across point A. Point M is the reflection of point E across point D. Line V passes through points F and D. Point T is the reflection of point K across line V. What is the length of segment TM? Expres... | 36.66 | MATH |
[
{
"content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 8. Let S be the perpendicular bisector of segment IH. Let Y be the reflection of line S through point D. Line R is the reflection of line Y across point F. Point T is the reflection of point L across point G. Point X is the ref... | 10.37 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center Z and circumradius 9. Let U be the midpoint of segment ZG. Let Q be the angle bisector of angle ACI. Let O be the line through point A parallel to line Q. Let M be the reflection of line O through point U. Point N is the reflection of point Z across lin... | 22.37 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center L and circumradius 5. Point G is the midpoint of segment AD. Let T be the reflection of point C across point E. Let Y be the reflection of point G across point T. Find the length of segment YC. Express your answer as a decimal number rounded to 2 decimal places... | 31.84 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Q and circumradius 9. Let P be the line through points D and H. Line Y passes through point G perpendicular to line P. Point Z lies on line Y. Line I passes through points D and A. Point U is the reflection of point Z across line I. What is the measure of ... | 1.96 | MATH |
[
{
"content": "ABDEF is a regular 5-gon with center C and circumradius 4. Let J be the reflection of point F across point A. Line M is the perpendicular bisector of segment BF. Line Y passes through point J parallel to line M. Let G be the line through point D perpendicular to line Y. Point N is the reflection o... | 16.35 | MATH |
[
{
"content": "Let ABCDEFHIJ be a regular 9-gon with center G and circumradius 7. Let K be the circumcircle of polygon ABCDEFHIJ. Point N is the midpoint of segment CI. Point R is the midpoint of segment EH. Let Z be the line through point F perpendicular to segment CI. Let S be the reflection of circle K across... | 14.16 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center O and circumradius 2. Line N is the angle bisector of angle CGB. Let L be the line through point C parallel to line N. Let J be the line through point H parallel to line L. Point M is the reflection of point A across line J. What is the distance between po... | 0.6 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center M and circumradius 5. Let K be the line through points M and G. Let S be the line through point A parallel to line K. Point T is the reflection of point F across point E. Point P is the reflection of point T across line S. Point H is the reflection of poi... | 24.05 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 3. Point Q is obtained by rotating point F by angle pi/6 about point C. Line Z is the angle bisector of angle BAF. Line I is the reflection of line Z across point B. Point U is the reflection of point A across point F. Point V is the r... | 16.41 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center V and circumradius 3. Let W be the rotation of point J by angle 7pi/12 around point I. Let M be the midpoint of segment DW. Point Y is the reflection of point W across point J. Line O passes through point G parallel to segment JV. Line N passes throug... | 12.7 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center S and circumradius 12. Point Z is the midpoint of segment DA. Point G is the reflection of point B across segment CE. Let P be the midpoint of segment CG. Point R is the reflection of point A across point P. What is the length of segment RZ? Express your answer... | 41.33 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center N and circumradius 4. Line H passes through points D and B. Let J be the line through points A and B. Line R passes through point F parallel to line H. Lines J and R intersect at point Z. Let V be the circumcircle of polygon ABCDEF. Let I be the inversion of... | 2.27 | MATH |
[
{
"content": "BCDEFG is a regular hexagon with center A and circumradius 3. Let V be the reflection of point A across point E. Line X is the angle bisector of angle VGD. Let I be the reflection of line X through point D. Point M is the reflection of point E across line I. What is the distance between points G a... | 10.57 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 3. Point U is on segment FB. Point Z is the reflection of point A across segment DC. What is the measure of angle UBZ, in radians? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex fo... | 1.96 | MATH |
[
{
"content": "ABCD is a square with center N and circumradius 4. Line M passes through point D perpendicular to segment CB. Point U is the reflection of point N across point D. Line E is the reflection of line M across point N. Point J is the reflection of point N across line E. What is the distance between poi... | 12.65 | MATH |
[
{
"content": "Let ABDE be a square with center C and circumradius 7. Line W is the perpendicular bisector of segment AC. Point R is the midpoint of segment DB. Point S is the reflection of point R across line W. Let I be the reflection of point E across point B. Find the distance between points S and I. Express... | 20.41 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center Y and circumradius 4. Point W is the midpoint of segment DG. Let L be the rotation of point C by angle 5pi/6 around point B. Line R is the perpendicular bisector of segment BW. Let Z be the midpoint of segment LC. Point V is the reflection of point E ... | 2.35 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center P and circumradius 10. Let X be the circumcircle of polygon ABCDEFGHIJK. Point N is the reflection of point C across point F. Let V be the inversion of point N in circle X. Point O is the midpoint of segment VP. What is the length of segment IO? Express ... | 9.61 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center J and circumradius 8. Let P be the reflection of point B across point D. Point Q is the midpoint of segment PE. Point N is the reflection of point B across segment QC. What is the measure of angle NDE, in radians? Express your answer as a decimal number roun... | 2.62 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center I and circumradius 4. Let O be the circumcircle of polygon ABCDE. Let U be the reflection of circle O through point D. Point T is the midpoint of segment BC. Let J be the inversion of point I in circle U. What is the length of segment TJ? Express your answer as... | 7.65 | MATH |
[
{
"content": "Let ABCD be a square with center Z and circumradius 7. Point U is the midpoint of segment BZ. Let W be the reflection of point U across point C. Point K is the midpoint of segment WZ. Find the length of segment KA. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the... | 14.11 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center T and circumradius 6. Let K be the rotation of point F by angle 3pi/4 around point G. Let Z be the angle bisector of angle DKB. Line Y is the reflection of line Z across point J. Line V is the reflection of line Y across point H. Point Q is the reflection... | 12.89 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center S and circumradius 8. Let F be the angle bisector of angle SBD. Line P passes through points C and E. Line Z is the reflection of line P across line F. Lines P and Z intersect at point J. What is the distance between points J and E? Express your answer as a dec... | 7.75 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center W and circumradius 4. Point O is the midpoint of segment AB. Point P is the reflection of point H across point F. Line J is the perpendicular bisector of segment FO. Point V is the reflection of point C across line J. What is the distance between points V ... | 6.11 | MATH |
[
{
"content": "ABCD is a square with center H and circumradius 5. Point J is obtained by rotating point B by angle pi/12 about point D. Point F is obtained by rotating point D by angle 3pi/4 about point J. Let R be the circumcircle of polygon ABCD. Line M is the perpendicular bisector of segment BD. Point S is t... | 30.32 | MATH |
[
{
"content": "Let ABCDEFGHIKL be a regular 11-gon with center J and circumradius 6. Let X be the line through points A and C. Let M be the line through point I parallel to line X. Segment LH and line M intersect at point Q. Find the distance between points Q and H. Express your answer as a decimal number rounde... | 2.01 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center O and circumradius 3. Point Y is obtained by rotating point C by angle pi/12 about point D. Let L be the reflection of point B across point A. Line R passes through point H parallel to segment FE. Point N is on segment FE. Line P is the reflection of line ... | 31.93 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center M and circumradius 11. Line O passes through points L and H. Point Q is the intersection of line O and segment KE. Point X is the midpoint of segment GJ. What is the distance between points X and Q? Express your answer as a decimal number rounded... | 8.68 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center M and circumradius 2. Point P is the midpoint of segment EA. Point Z is the reflection of point B across point E. Let H be the midpoint of segment ZP. Point Q is the midpoint of segment AH. What is the length of segment BQ? Express your answer as a decimal ... | 3.67 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center Z and circumradius 11. Let M be the midpoint of segment IF. Point N is the midpoint of segment EM. Point X is the reflection of point F across point J. What is the length of segment XN? Express your answer as a decimal number rounded to 2 decimal places.\... | 37.67 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center N and circumradius 6. Point X is the reflection of point B across point C. Let O be the angle bisector of angle DNE. Let Z be the line through point X perpendicular to line O. Let U be the line through point N parallel to line Z. Point H is the reflection o... | 23.12 | MATH |
[
{
"content": "ABCDEFGHJK is a regular 10-gon with center I and circumradius 5. Let P be the circumcircle of polygon ABCDEFGHJK. Let W be the reflection of circle P through point G. Let V be the inversion of point A in circle W. Let R be the angle bisector of angle FVE. Point N is the reflection of point J acros... | 12.26 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center L and circumradius 4. Let K be the line through points B and F. Let N be the perpendicular bisector of segment FA. Line U is the reflection of line N across point E. Line J is the reflection of line K across point E. Line V passes through points D and ... | 10.45 | MATH |
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