messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 1. Let Q be the circumcircle of polygon ABCDEF. Circle X is the reflection of circle Q across point E. Point W is the inversion of point F with respect to circle X. Point O is the inversion of point W with respect to circle Q. What is ... | 0.87 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center G and circumradius 3. Let O be the midpoint of segment BD. Point Z is the reflection of point A across segment DB. Point H is the reflection of point C across point Z. Find the length of segment HO. Express your answer as a decimal number rounded to 2 decima... | 6.87 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center U and circumradius 6. Let Q be the reflection of point K across point A. Let X be the midpoint of segment UB. Let Z be the midpoint of segment FQ. Find the length of segment ZX. Express your answer as a decimal number rounded to 2 decimal places.\n\n... | 2.69 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center T and circumradius 9. Point Z is the reflection of point G across point B. Point L is the midpoint of segment FZ. Point K is the midpoint of segment DZ. Find the distance between points K and L. Express your answer as a decimal number rounded to 2 dec... | 5.29 | MATH |
[
{
"content": "ABCDFGHIJK is a regular 10-gon with center E and circumradius 9. Let X be the line through points B and J. Point N is the intersection of segment AD and line X. Point P is the reflection of point J across point A. Let S be the midpoint of segment NB. Find the length of segment PS. Express your ans... | 9.79 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center U and circumradius 2. Let T be the reflection of point G across point B. Let S be the midpoint of segment GB. Point R is the reflection of point T across point S. Find the length of segment RA. Express your answer as a decimal number rounded to 2 decim... | 6.4 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center S and circumradius 12. Let I be the perpendicular bisector of segment BS. Point P is the reflection of point E across line I. Line X passes through point D perpendicular to line I. Line L passes through point E perpendicular to line X. Point W is the reflection... | 48.49 | MATH |
[
{
"content": "Let ABDEFGHIJKLM be a regular dodecagon with center C and circumradius 5. Let Q be the circumcircle of polygon ABDEFGHIJKLM. Point T is the reflection of point B across point K. Line V passes through points C and F. Let Y be the line through point T perpendicular to line V. Point Z is the reflecti... | 4.66 | MATH |
[
{
"content": "ABCDEFGHIK is a regular 10-gon with center J and circumradius 3. Let P be the circumcircle of polygon ABCDEFGHIK. Let N be the perpendicular bisector of segment JE. Circle R is the reflection of circle P across point H. Point Q is the reflection of point D across line N. Circle T is the reflection... | 7.56 | MATH |
[
{
"content": "Let ABCDEFGHIJKM be a regular dodecagon with center L and circumradius 6. Point Q is the midpoint of segment HJ. Let O be the midpoint of segment EC. Point T is the reflection of point B across point O. Find the distance between points Q and T. Express your answer as a decimal number rounded to 2 ... | 12.17 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center O and circumradius 2. Line I passes through point C parallel to segment OA. Point Z is the reflection of point D across line I. Point T is the midpoint of segment ZE. Find the distance between points O and T. Express your answer as a decimal number rounded t... | 1.73 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center X and circumradius 12. Let T be the circumcircle of polygon ABCDEFGHIJKL. Circle Y is the reflection of circle T across point E. Circle V is the reflection of circle T across point K. Point S is the inversion of point F with respect to circle V. ... | 17.99 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Z and circumradius 1. Let T be the midpoint of segment CE. Let U be the angle bisector of angle TFB. Let S be the line through point C perpendicular to line U. Point R is the reflection of point F across line S. What is the length of segment BR? Express yo... | 1.88 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center G and circumradius 11. Point L is the reflection of point A across point D. Let V be the perpendicular bisector of segment CF. Let M be the line through point L perpendicular to line V. Point X is the reflection of point D across line M. What is the distance... | 47.95 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 10. Point V is the midpoint of segment HF. Let R be the perpendicular bisector of segment AV. Point J is the reflection of point G across line R. Find the distance between points G and J. Express your answer as a decimal number round... | 15.63 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center P and circumradius 8. Point R is the midpoint of segment AF. Let K be the perpendicular bisector of segment BR. Let Z be the reflection of line K through point A. Point H is the reflection of point R across point D. Point I is the reflection of point H acros... | 18.14 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center G and circumradius 11. Point R is obtained by rotating point G by angle pi/4 about point B. Let T be the midpoint of segment ER. Let M be the circumcircle of polygon ABCDEF. Let O be the midpoint of segment FT. Point V is the reflection of point D across... | 24.31 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center U and circumradius 1. Point Q is the midpoint of segment UE. Point G is the midpoint of segment QC. Point T is the reflection of point G across point C. Point X is the reflection of point T across segment AQ. Find the distance between points T and X. Express... | 3.93 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center Y and circumradius 6. Let T be the perpendicular bisector of segment DB. Line Z is the angle bisector of angle HGA. Line L is the reflection of line Z across line T. Let W be the rotation of point Y by angle 11pi/12 around point A. Let R be the circumc... | 23.26 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center K and circumradius 2. Point N is obtained by rotating point B by angle 11pi/12 about point C. Let W be the perpendicular bisector of segment NE. Line Q passes through point I perpendicular to line W. Let M be the line through point C parallel to line ... | 2.44 | MATH |
[
{
"content": "ABDEFG is a regular hexagon with center C and circumradius 8. Let K be the line through points A and D. Point X is the reflection of point F across point B. Let L be the reflection of point G across point D. Point U is the reflection of point X across segment EB. Point T is the reflection of point... | 40.0 | MATH |
[
{
"content": "ACDEFGHIJKLM is a regular dodecagon with center B and circumradius 11. Line O passes through points A and F. Point S is the reflection of point C across point D. Line W is the perpendicular bisector of segment KS. Let Y be the reflection of line W across line O. Point Z is the intersection of line... | 20.24 | MATH |
[
{
"content": "Let ABCDEFHI be a regular octagon with center G and circumradius 4. Line X passes through points I and G. Point M is the reflection of point I across point F. Point U is the reflection of point M across line X. Let T be the midpoint of segment UC. What is the length of segment TM? Express your ans... | 13.43 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center K and circumradius 4. Let Y be the midpoint of segment CK. Let W be the reflection of point B across point A. Point R is the reflection of point Y across segment DW. What is the length of segment CR? Express your answer as a decimal number rounded to 2 deci... | 8.56 | MATH |
[
{
"content": "ABCEFGHI is a regular octagon with center D and circumradius 12. Line X is the angle bisector of angle FBI. Line M is the reflection of line X across point H. Point W is the reflection of point D across line M. Point Y is the midpoint of segment WG. Find the length of segment YC. Express your answ... | 22.88 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center S and circumradius 8. Line O passes through point D perpendicular to segment DJ. Point Z is the reflection of point S across line O. Let K be the reflection of point I across point B. Find the length of segment KZ. Express your answer as a decimal number ... | 19.98 | MATH |
[
{
"content": "ABCDFGHI is a regular octagon with center E and circumradius 7. Let J be the line through points I and C. Point T is the reflection of point B across line J. Let M be the midpoint of segment AT. Point R is the reflection of point D across point M. Find the distance between points R and A. Express ... | 4.1 | MATH |
[
{
"content": "ABCDEGHIJ is a regular 9-gon with center F and circumradius 9. Let O be the reflection of point E across point H. Let W be the angle bisector of angle CBG. Point Q is the reflection of point F across line W. Let Y be the reflection of line W through point Q. Point T is the reflection of point F ac... | 53.38 | MATH |
[
{
"content": "ABCDEFGIJ is a regular 9-gon with center H and circumradius 10. Let V be the line through points H and E. Line K is the perpendicular bisector of segment CH. Let N be the reflection of line K through point D. Point U is the reflection of point A across line N. Point Y is the intersection of lines ... | 68.92 | MATH |
[
{
"content": "Let ABCDEFGHI be a regular 9-gon with center U and circumradius 5. Point S is the midpoint of segment UD. Point O is the reflection of point I across point D. Line Q passes through point O perpendicular to segment ID. Line P is the reflection of line Q across point B. Line Y is the reflection of l... | 89.45 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Y and circumradius 10. Point U is obtained by rotating point B by angle 3pi/4 about point F. Point K is the reflection of point U across point F. Point Z is the reflection of point U across point B. Line N is the perpendicular bisector of segment BK. Point W... | 38.46 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center F and circumradius 1. Let L be the angle bisector of angle ACF. Point W is the midpoint of segment ED. Point H is the reflection of point W across line L. Point X is the midpoint of segment DC. Point J is the midpoint of segment HX. Find the distance betwee... | 0.85 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center T and circumradius 3. Point U is the midpoint of segment BD. Point N is the reflection of point A across segment DU. Point Z is the midpoint of segment ND. Let R be the midpoint of segment ZE. Find the length of segment RN. Express your answer as a decimal ... | 5.11 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center K and circumradius 3. Let P be the line through points C and B. Line L is the angle bisector of angle KFG. Line Y is the reflection of line L across line P. Point V is the reflection of point B across line Y. What is the distance between points H and ... | 14.94 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center P and circumradius 12. Let X be the circumcircle of polygon ABCDEFGH. Point O is the midpoint of segment CB. Let K be the inversion of point O in circle X. Let Z be the midpoint of segment KF. What is the distance between points Z and E? Express your a... | 10.39 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center M and circumradius 8. Let F be the angle bisector of angle CBM. Let S be the line through point M perpendicular to line F. Let Z be the reflection of line S through point C. Let Q be the line through point E parallel to line Z. Line N is the reflection of line ... | 11.0 | MATH |
[
{
"content": "ACDEF is a regular 5-gon with center B and circumradius 6. Let O be the circumcircle of polygon ACDEF. Let Y be the reflection of circle O through point D. Let K be the reflection of point F across point E. Let U be the inversion of point A in circle Y. Let R be the line through point D parallel t... | 10.42 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 3. Let P be the circumcircle of polygon ABCDEF. Point N is the reflection of point A across segment CE. Let R be the reflection of point C across point N. Point S is the inversion of point R with respect to circle P. Find the length of seg... | 2.2 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Y and circumradius 2. Let Z be the reflection of point D across point Y. Point S is the reflection of point A across segment BZ. Let W be the midpoint of segment ZB. Find the distance between points W and S. Express your answer as a decimal number rounded t... | 1.77 | MATH |
[
{
"content": "ABCD is a square with center H and circumradius 7. Let T be the midpoint of segment AB. Let E be the circumcircle of polygon ABCD. Let G be the inversion of point T in circle E. Point X is the reflection of point G across point H. Point Q is the reflection of point A across point X. Find the dista... | 15.65 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center L and circumradius 12. Let Q be the rotation of point G by angle pi/4 around point F. Point T is the midpoint of segment BJ. Let X be the circumcircle of polygon ABCDEFGHIJ. Let R be the midpoint of segment JF. Let N be the inversion of point T in circle ... | 34.47 | MATH |
[
{
"content": "Let ABCDEGHIJ be a regular 9-gon with center F and circumradius 5. Point L is the midpoint of segment FJ. Let P be the midpoint of segment LC. Point W is the midpoint of segment PI. Let U be the line through points W and A. Segment BH and line U intersect at point N. What is the distance between p... | 2.3 | MATH |
[
{
"content": "ABCD is a square with center N and circumradius 3. Let F be the rotation of point N by angle 7pi/12 around point B. Let M be the perpendicular bisector of segment NC. Let U be the perpendicular bisector of segment AC. Point Q is the reflection of point F across line M. Line L passes through point ... | 8.8 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 3. Let W be the line through point H perpendicular to segment GE. Point T is the reflection of point C across line W. Let J be the midpoint of segment FT. Point R is the reflection of point J across segment GE. What is the distance b... | 2.57 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center I and circumradius 6. Let O be the angle bisector of angle ACD. Let U be the circumcircle of polygon ABCDEFGH. Circle L is the reflection of circle U across line O. Let T be the inversion of point B in circle L. Let S be the midpoint of segment BH. Wha... | 3.73 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center P and circumradius 2. Line O is the angle bisector of angle HJP. Point U is the reflection of point C across line O. Let Z be the midpoint of segment KU. Point R is the midpoint of segment BZ. What is the distance between points R and A? Express your... | 1.83 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 2. Let T be the line through points B and G. Let M be the reflection of point G across point D. Let W be the reflection of point M across point E. Point K is the reflection of point W across line T. What is the length of segment KA? Ex... | 6.0 | MATH |
[
{
"content": "Let ABCDEFGHIK be a regular 10-gon with center J and circumradius 8. Line R is the perpendicular bisector of segment AH. Let Y be the line through point F parallel to line R. Point P is the midpoint of segment CG. Point X is the midpoint of segment DG. Point S is the reflection of point X across l... | 9.53 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 9. Line Y is the angle bisector of angle HND. Line O is the reflection of line Y across point G. Point L is the reflection of point E across line O. Point I is the intersection of segment LF and line O. Find the distance between poin... | 21.19 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center K and circumradius 9. Line U passes through points A and E. Let S be the reflection of point D across point E. Line Y passes through point F perpendicular to line U. Point R is the reflection of point S across line Y. Let P be the midpoint of segment SF. Wha... | 11.91 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center M and circumradius 9. Let P be the circumcircle of polygon ABCDEFG. Point J is the midpoint of segment BA. Let O be the inversion of point J in circle P. What is the distance between points O and J? Express your answer as a decimal number rounded to 2 dec... | 1.88 | MATH |
[
{
"content": "Let ABCDEGHIJKLM be a regular dodecagon with center F and circumradius 9. Point W is the reflection of point E across point J. Let O be the line through point I parallel to segment LM. Point S is the reflection of point W across line O. What is the length of segment MS? Express your answer as a de... | 34.63 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center Q and circumradius 4. Point L is the reflection of point D across point A. Point Y is the reflection of point L across segment CE. Let Z be the midpoint of segment CE. What is the distance between points Z and Y? Express your answer as a decimal number rounded ... | 12.62 | MATH |
[
{
"content": "Let ABCDEFGHIKLM be a regular dodecagon with center J and circumradius 12. Let Z be the line through points M and A. Point X is the reflection of point I across point B. Let Q be the line through point F parallel to line Z. Point U is the reflection of point X across line Q. What is the length of ... | 63.34 | MATH |
[
{
"content": "Let ABCEFGHIJK be a regular 10-gon with center D and circumradius 8. Let S be the line through points A and J. Point T is the midpoint of segment CE. Let M be the line through point F perpendicular to line S. Point O is the reflection of point T across line M. What is the length of segment OI? Exp... | 7.09 | MATH |
[
{
"content": "Let ABCDEFGHJKL be a regular 11-gon with center I and circumradius 11. Let Q be the rotation of point A by angle 2pi/3 around point I. Point M is the reflection of point L across segment JD. Let Y be the midpoint of segment JQ. Find the length of segment MY. Express your answer as a decimal number... | 10.3 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 12. Let Y be the midpoint of segment BD. Point Q is the reflection of point Y across point C. Let K be the circumcircle of polygon ABCDF. Point R is the inversion of point Y with respect to circle K. Find the length of segment RQ. Express you... | 18.54 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Z and circumradius 5. Let N be the line through points E and F. Point V is the reflection of point A across line N. Point T is the reflection of point V across segment FD. What is the distance between points V and T? Express your answer as a decimal number... | 17.07 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center T and circumradius 3. Let X be the circumcircle of polygon ABCDEFGHIJKL. Let Z be the reflection of point D across point J. Point W is the reflection of point J across point E. Line N passes through point L parallel to segment DZ. Circle V is the ref... | 7.67 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center T and circumradius 12. Let U be the midpoint of segment AJ. Let X be the reflection of point U across point L. Let O be the midpoint of segment JX. Point S is the midpoint of segment OF. Let Z be the reflection of point K across point E. Find the... | 36.61 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center S and circumradius 10. Let X be the line through points A and B. Point Q is the reflection of point A across point B. Line U is the reflection of line X across point C. Line W passes through point H parallel to line U. Point P is the reflection of po... | 31.62 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center S and circumradius 3. Line J is the perpendicular bisector of segment FG. Line W passes through point A perpendicular to line J. Point Z is the reflection of point B across point E. Line M is the reflection of line W across point B. Point R is the refl... | 6.65 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center P and circumradius 9. Let Z be the reflection of point B across point J. Let Q be the midpoint of segment DA. Point V is the midpoint of segment EQ. What is the length of segment ZV? Express your answer as a decimal number rounded to 2 decimal places... | 29.69 | MATH |
[
{
"content": "Let ABDEFGHIJKLM be a regular dodecagon with center C and circumradius 3. Let Y be the perpendicular bisector of segment HE. Line S passes through point J parallel to line Y. Point R is the reflection of point M across line S. Let W be the reflection of point R across point D. What is the distance... | 11.69 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center T and circumradius 10. Line Y passes through points D and A. Let V be the reflection of line Y through point B. Point X is the reflection of point T across line V. Line R passes through points I and X. Point U is the reflection of point J across line ... | 3.97 | MATH |
[
{
"content": "ABCDEFHIJKLM is a regular dodecagon with center G and circumradius 4. Point V is the midpoint of segment KE. Line U is the angle bisector of angle IHV. Point W is the reflection of point E across line U. Point O is the reflection of point B across point W. What is the distance between points V and... | 17.96 | MATH |
[
{
"content": "ABDEFGH is a regular 7-gon with center C and circumradius 8. Let Q be the circumcircle of polygon ABDEFGH. Point R is the midpoint of segment BH. Let I be the reflection of circle Q through point F. Point W is the inversion of point R with respect to circle I. What is the length of segment EW? Exp... | 10.3 | MATH |
[
{
"content": "ABCDEFGHIJL is a regular 11-gon with center K and circumradius 12. Let Q be the circumcircle of polygon ABCDEFGHIJL. Line S passes through points E and H. Let M be the line through point G perpendicular to line S. Let T be the reflection of circle Q across line M. Point X is the reflection of poin... | 11.66 | MATH |
[
{
"content": "ABDEFGHI is a regular octagon with center C and circumradius 8. Let T be the perpendicular bisector of segment AC. Line R is the reflection of line T across point C. Line L is the reflection of line R across line T. Point Y is the reflection of point I across line L. Find the length of segment CY.... | 19.2 | MATH |
[
{
"content": "Let ABCDEFHI be a regular octagon with center G and circumradius 3. Point R is the midpoint of segment IH. Point K is the midpoint of segment DR. Point O is the midpoint of segment CA. What is the distance between points O and K? Express your answer as a decimal number rounded to 2 decimal places.... | 2.66 | MATH |
[
{
"content": "ABCDFGHIJKLM is a regular dodecagon with center E and circumradius 5. Line O passes through point K parallel to segment HG. Line P passes through point C perpendicular to line O. Point Y is the reflection of point J across line P. Point X is the reflection of point Y across segment HG. Find the le... | 21.6 | MATH |
[
{
"content": "ACDEFG is a regular hexagon with center B and circumradius 3. Line I is the angle bisector of angle DBE. Point N is obtained by rotating point G by angle 5pi/12 about point B. Let M be the perpendicular bisector of segment AB. Point H lies on line I at distance 3 from point A. Let V be the line th... | 8.54 | MATH |
[
{
"content": "Let BCDEFGHI be a regular octagon with center A and circumradius 5. Let O be the line through points F and I. Let Q be the line through point H parallel to line O. Let R be the line through point B parallel to line O. Point S is the reflection of point C across line R. Point X is the reflection of... | 13.61 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center Z and circumradius 9. Line I passes through points B and Z. Let H be the reflection of point D across point B. Let Y be the line through point B perpendicular to line I. Line P passes through points Z and C. Let T be the reflection of line Y through point H. Li... | 132.0 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Y and circumradius 4. Line N is the perpendicular bisector of segment YB. Point Z is the reflection of point A across line N. Point T is the reflection of point Z across segment DY. Let H be the midpoint of segment ET. Point F is the reflection of point D a... | 10.47 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center T and circumradius 11. Point X is the midpoint of segment BG. Line Q passes through points X and A. Point M is the intersection of line Q and segment FD. Let J be the reflection of point E across point H. Find the length of segment MJ. Express your ans... | 36.15 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center W and circumradius 12. Let R be the reflection of point G across point L. Let Y be the line through points D and G. Segment ER and line Y intersect at point Q. Find the distance between points Q and H. Express your answer as a decimal number roun... | 16.43 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center W and circumradius 10. Let V be the line through points E and F. Let L be the line through point C perpendicular to line V. Let P be the line through points E and A. Let S be the reflection of line P across line L. Point M is the reflection of point A ac... | 28.8 | MATH |
[
{
"content": "Let ABCD be a square with center M and circumradius 1. Line Z is the perpendicular bisector of segment DM. Let I be the midpoint of segment BA. Let H be the circumcircle of polygon ABCD. Let K be the reflection of circle H across line Z. Point X is the inversion of point I with respect to circle K... | 1.41 | MATH |
[
{
"content": "Let ACDEF be a regular 5-gon with center B and circumradius 10. Point M is the midpoint of segment FB. Line W passes through point A perpendicular to segment CB. Point L is the reflection of point M across line W. Find the distance between points C and L. Express your answer as a decimal number ro... | 2.95 | MATH |
[
{
"content": "Let ABCDEFH be a regular 7-gon with center G and circumradius 4. Point W is obtained by rotating point D by angle 3pi/4 about point B. Let N be the reflection of point G across point D. Line Y is the perpendicular bisector of segment BC. Line K is the reflection of line Y across point N. Point O i... | 31.04 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center M and circumradius 12. Let X be the line through point G parallel to segment DH. Line L is the reflection of line X across point F. Point R is the reflection of point F across line L. Find the distance between points G and R. Express your answer as a decim... | 13.53 | MATH |
[
{
"content": "ABCDEFGHIJKM is a regular dodecagon with center L and circumradius 11. Let V be the line through points D and A. Point Q is obtained by rotating point M by angle pi/2 about point F. Let W be the circumcircle of polygon ABCDEFGHIJKM. Point X is the midpoint of segment JL. Circle U is the reflection... | 19.11 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center Z and circumradius 6. Line V passes through point A perpendicular to segment JD. Let W be the line through point H perpendicular to line V. Point S is the reflection of point D across line W. Find the distance between points S and Z. Express your answer ... | 12.46 | MATH |
[
{
"content": "BCDEFGHIJK is a regular 10-gon with center A and circumradius 1. Let U be the line through points H and C. Let O be the midpoint of segment EA. Line V passes through point G parallel to line U. Point Z is the reflection of point O across line V. Point Y is the reflection of point A across segment ... | 0.36 | MATH |
[
{
"content": "EY = 2. Let ABCDFGHIJ be a regular 9-gon with center Y and circumradius 9. Point N is on segment YJ. Let S be the circumcircle of polygon ABCDFGHIJ. Point M is the inversion of point N with respect to circle S. What is the measure of angle HYM, in radians? Express your answer as a decimal number r... | 1.4 | MATH |
[
{
"content": "Let ABCDFGHI be a regular octagon with center E and circumradius 9. Let V be the angle bisector of angle ECG. Point O is the midpoint of segment IA. Point X is the reflection of point I across line V. Point N is the reflection of point H across point X. What is the length of segment NO? Express yo... | 31.9 | MATH |
[
{
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 9. Point S is obtained by rotating point F by angle 7pi/12 about point A. Let Z be the rotation of point L by angle 5pi/6 around point G. Let R be the line through points M and D. Point X is the reflection of point Z across point D... | 28.42 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center L and circumradius 2. Let P be the circumcircle of polygon ABCDE. Line O is the angle bisector of angle LCA. Circle M is the reflection of circle P across line O. Let W be the perpendicular bisector of segment LC. Circle R is the reflection of circle M acro... | 5.89 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center H and circumradius 5. Let L be the vector from point C to point A. Point Q is the translation of point F by vector L. Let Z be the reflection of point Q across point D. Let K be the circumcircle of polygon ABCDEF. Let I be the midpoint of segment QA. Let W b... | 8.34 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center M and circumradius 12. Let L be the reflection of point F across point C. Let O be the reflection of point D across point B. Point Y is the midpoint of segment LM. What is the length of segment YO? Express your answer as a decimal number rounded to 2 dec... | 33.41 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center V and circumradius 3. Let O be the angle bisector of angle LAI. Point N is the midpoint of segment HG. Let W be the perpendicular bisector of segment NV. Point M is the reflection of point J across line O. Let Y be the reflection of line W throug... | 5.92 | MATH |
[
{
"content": "ABCDEFGHIJK is a regular 11-gon with center X and circumradius 6. Let U be the line through points I and C. Point N is the reflection of point A across point H. Segment JD and line U intersect at point R. Find the length of segment RN. Express your answer as a decimal number rounded to 2 decimal p... | 17.31 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center J and circumradius 8. Point X is the reflection of point A across point D. Let S be the circumcircle of polygon ABCDE. Let Z be the inversion of point X in circle S. Point T is the midpoint of segment AD. What is the length of segment ZT? Express your answer as... | 3.52 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center I and circumradius 10. Line Q is the perpendicular bisector of segment IC. Line T is the reflection of line Q across point G. Line P passes through points D and A. Lines T and P intersect at point M. Let L be the perpendicular bisector of segment MI. Point K ... | 38.06 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center W and circumradius 11. Let O be the line through points D and B. Point X is the reflection of point H across line O. Point S is the reflection of point F across line O. Point K is the reflection of point S across segment WX. What is the length of segment A... | 16.77 | MATH |
[
{
"content": "FU = 3. Let ABCDE be a regular 5-gon with center U and circumradius 2. Point I is the midpoint of segment CD. Point R is the midpoint of segment IC. Point O is the midpoint of segment IR. Point G is the reflection of point D across point E. Find the length of segment GO. Express your answer as a d... | 5.34 | MATH |
[
{
"content": "ABCDEFGHIJ is a regular 10-gon with center P and circumradius 3. Let V be the reflection of point D across point F. Line X passes through point G perpendicular to segment BV. Point S is the reflection of point J across line X. What is the distance between points E and S? Express your answer as a d... | 8.16 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center L and circumradius 8. Let H be the midpoint of segment FD. Let K be the midpoint of segment DC. Point Z is the reflection of point K across segment BH. What is the measure of angle BAZ, in radians? Express your answer as a decimal number rounded to 2 dec... | 2.09 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center P and circumradius 1. Let K be the midpoint of segment GP. Line X is the perpendicular bisector of segment AP. Point N is obtained by rotating point A by angle 2pi/3 about point P. Point T is the reflection of point D across point H. Line J passes through ... | 1.61 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.