messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Let ABCEFGHIJKLM be a regular dodecagon with center D and circumradius 5. Let V be the midpoint of segment BF. Let X be the midpoint of segment DV. Line R is the perpendicular bisector of segment LJ. Point O is the reflection of point X across line R. Find the distance between points O and G. Expr... | 3.95 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center G and circumradius 9. Line N is the angle bisector of angle GDB. Point O is the reflection of point G across line N. Line F is the angle bisector of angle CAO. Line H passes through point D parallel to line F. Let L be the midpoint of segment BD. Point T is... | 13.59 | MATH |
[
{
"content": "Let BCDEFG be a regular hexagon with center A and circumradius 4. Point X is the reflection of point E across point F. Let S be the midpoint of segment EA. Let N be the midpoint of segment XS. What is the length of segment ND? Express your answer as a decimal number rounded to 2 decimal places.\n\... | 7.0 | MATH |
[
{
"content": "Let ABCDEFGHJKLM be a regular dodecagon with center I and circumradius 2. Let S be the reflection of point D across point L. Let Q be the midpoint of segment SL. Point R is the reflection of point H across point K. What is the length of segment RQ? Express your answer as a decimal number rounded t... | 0.64 | MATH |
[
{
"content": "ABCDEGHIJ is a regular 9-gon with center F and circumradius 10. Let T be the reflection of point B across point I. Line L is the angle bisector of angle CGD. Let N be the reflection of point F across point T. Point Z is the reflection of point N across line L. Find the distance between points Z an... | 48.84 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center K and circumradius 9. Let H be the reflection of point E across point C. Let L be the line through point H parallel to segment AF. Point R is the reflection of point D across line L. Point T is the midpoint of segment AF. Point Y is the reflection of poi... | 1.05 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Y and circumradius 6. Line O is the angle bisector of angle KCE. Let N be the line through point Y parallel to line O. Let U be the reflection of line N across line O. Let Z be the angle bisector of angle BFJ. Let W be the reflection of line Z ac... | 5.8 | MATH |
[
{
"content": "Let BCDEFGHIJKLM be a regular dodecagon with center A and circumradius 3. Point U is the midpoint of segment LE. Point Q is the reflection of point B across segment LE. Let T be the reflection of point G across point Q. What is the length of segment UT? Express your answer as a decimal number roun... | 3.91 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 8. Line S passes through points B and E. Line S and segment GD intersect at point Y. Point W is the midpoint of segment AY. Find the length of segment FW. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent ... | 3.46 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center K and circumradius 8. Line O passes through points A and D. Point M is the reflection of point B across point D. Let Z be the line through points E and D. Let J be the reflection of line Z across line O. Point Y is the reflection of point M across line J... | 8.0 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center T and circumradius 5. Point S is obtained by rotating point C by angle 3pi/4 about point B. Point F is the midpoint of segment CE. Let M be the midpoint of segment DB. Point G is the reflection of point F across segment DS. Find the distance between points ... | 3.07 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center J and circumradius 2. Point M is the reflection of point A across point E. Point G is the intersection of segments MJ and AD. Point V is the reflection of point A across segment MJ. Find the length of segment GV. Express your answer as a decimal number rounded ... | 2.25 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center Z and circumradius 12. Point I is obtained by rotating point A by angle 3pi/4 about point B. Let V be the line through points Z and B. Line P passes through point I parallel to line V. Let H be the reflection of line P across line V. Point T is the intersection... | 13.94 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center K and circumradius 1. Let L be the circumcircle of polygon ABCDEFGHIJ. Let V be the angle bisector of angle FAJ. Point P is the reflection of point C across line V. Point X is the inversion of point P with respect to circle L. Find the distance betwee... | 0.49 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center L and circumradius 4. Let Q be the midpoint of segment AB. Point M is the reflection of point D across point Q. Point V is the reflection of point Q across segment EM. What is the distance between points D and V? Express your answer as a decimal number roun... | 9.61 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center K and circumradius 11. Let X be the midpoint of segment DG. Point Z is the reflection of point X across point K. Point U is the midpoint of segment FZ. What is the distance between points B and U? Express your answer as a decimal number rounded to 2 de... | 14.58 | MATH |
[
{
"content": "Let ABCEFGHI be a regular octagon with center D and circumradius 11. Let X be the reflection of point I across point H. Point L is the midpoint of segment HX. Let K be the reflection of point A across point H. Find the length of segment KL. Express your answer as a decimal number rounded to 2 deci... | 11.78 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center R and circumradius 8. Let Z be the circumcircle of polygon ABCDEFGHI. Let X be the reflection of circle Z through point G. Let Q be the midpoint of segment DE. Point M is the midpoint of segment CQ. Point Y is the inversion of point M with respect to circle... | 13.67 | MATH |
[
{
"content": "ABCDEFG is a regular 7-gon with center Z and circumradius 6. Let P be the reflection of point Z across point A. Let S be the rotation of point P by angle pi/4 around point C. Point O is the midpoint of segment EP. Let M be the perpendicular bisector of segment ZS. Line K passes through point C per... | 19.71 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center Q and circumradius 3. Let T be the reflection of point D across point C. Let J be the midpoint of segment QT. Let X be the reflection of point A across point J. What is the distance between points X and B? Express your answer as a decimal number rounded to 2... | 5.2 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center X and circumradius 7. Let Q be the line through points F and D. Point K is the reflection of point C across segment FB. Point H is the reflection of point C across line Q. What is the measure of angle KCH, in radians? Express your answer as a decimal number ... | 2.09 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center W and circumradius 1. Let T be the perpendicular bisector of segment BW. Let K be the midpoint of segment FD. Line X passes through point G perpendicular to segment FD. Let P be the reflection of line X across line T. Line I is the perpendicular bisect... | 3.56 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center I and circumradius 6. Let W be the reflection of point A across point B. Point J is the midpoint of segment FB. Point Y is the reflection of point W across point F. Point V is the midpoint of segment JY. Point K is the midpoint of segment AE. What is the len... | 8.35 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center M and circumradius 8. Point T is the reflection of point D across point G. Line W is the angle bisector of angle TFG. Let U be the reflection of point A across point B. Point Y is the reflection of point U across line W. Find the distance between points Y ... | 22.63 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Q and circumradius 3. Point S is the midpoint of segment HQ. Line J is the perpendicular bisector of segment SG. Point Y is the reflection of point Q across line J. What is the length of segment HY? Express your answer as a decimal number rounded to 2 deci... | 3.63 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Y and circumradius 11. Let V be the midpoint of segment CD. Let Q be the midpoint of segment FB. Point U is the reflection of point B across segment VD. What is the measure of angle UQV, in radians? Express your answer as a decimal number rounded to 2 de... | 0.52 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center M and circumradius 11. Let L be the line through point C perpendicular to segment AC. Point T is the reflection of point F across line L. Let S be the reflection of point T across point A. Point Z is the reflection of point S across segment AC. What is... | 31.11 | MATH |
[
{
"content": "Let ABCDEFHIJK be a regular 10-gon with center G and circumradius 10. Point L is the reflection of point B across point F. Let Y be the reflection of point B across point L. Let V be the midpoint of segment YI. Find the distance between points B and V. Express your answer as a decimal number round... | 46.08 | MATH |
[
{
"content": "ABDEFGHI is a regular octagon with center C and circumradius 6. Let S be the rotation of point F by angle pi/12 around point B. Let K be the perpendicular bisector of segment DF. Line L passes through point F parallel to line K. Let U be the perpendicular bisector of segment HS. Let J be the refle... | 9.35 | MATH |
[
{
"content": "Let ABCDEG be a regular hexagon with center F and circumradius 2. Point H is the reflection of point A across point C. Point Q is the midpoint of segment GH. Let O be the reflection of point Q across point C. Point I is the midpoint of segment OB. What is the length of segment ID? Express your ans... | 3.12 | MATH |
[
{
"content": "Let BCDEF be a regular 5-gon with center A and circumradius 11. Let M be the reflection of point D across point C. Let X be the circumcircle of polygon BCDEF. Point L is the reflection of point F across point M. Point K is the inversion of point L with respect to circle X. Find the length of segme... | 11.26 | MATH |
[
{
"content": "BN = 10. Let ACDEFG be a regular hexagon with center N and circumradius 7. Let S be the reflection of point E across point C. Line L is the perpendicular bisector of segment DS. Let O be the line through points C and G. Point I is the reflection of point G across line L. Point J is the reflection ... | 16.09 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center O and circumradius 7. Point Y is the intersection of segments FK and OH. Point R is the reflection of point Y across point K. Point Z is the reflection of point E across point B. What is the length of segment ZR? Express your answer as a decimal numb... | 14.0 | MATH |
[
{
"content": "Let ACDEFGHIJK be a regular 10-gon with center B and circumradius 11. Let O be the line through points G and D. Line L passes through point A perpendicular to line O. Point M is the reflection of point I across point F. Point U is the reflection of point J across line L. Point V is the midpoint of... | 20.65 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center R and circumradius 7. Point M is the midpoint of segment CR. Let T be the circumcircle of polygon ABCDEFGH. Let J be the inversion of point M in circle T. What is the distance between points J and A? Express your answer as a decimal number rounded to 2 dec... | 15.65 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center U and circumradius 7. Point N is obtained by rotating point U by angle pi/12 about point A. Line M is the angle bisector of angle DAE. Line L passes through points N and E. Line F is the reflection of line L across line M. Point S is the reflection of point... | 3.96 | MATH |
[
{
"content": "Let LZ = 3. Let ABCDEFGHIJKM be a regular dodecagon with center Z and circumradius 4. Let R be the line through point D parallel to segment HZ. Point S is on line R. Point P is the reflection of point S across segment HZ. Find the distance between points P and S. Express your answer as a decimal n... | 6.93 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center Q and circumradius 6. Let W be the line through points A and D. Line P is the reflection of line W across point B. Point S is the reflection of point C across line P. Let T be the midpoint of segment SD. Find the distance between points T and C. Express ... | 3.0 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center S and circumradius 5. Let I be the circumcircle of polygon ABCDEF. Let H be the line through points A and C. Let M be the midpoint of segment ES. Let L be the reflection of circle I through point D. Let Q be the inversion of point A in circle L. Point R ... | 13.72 | MATH |
[
{
"content": "Let ABCDEFGHIK be a regular 10-gon with center J and circumradius 4. Line O is the perpendicular bisector of segment DK. Line T passes through point H parallel to line O. Point P is the midpoint of segment KF. Point V is the reflection of point P across line T. What is the length of segment DV? Ex... | 8.09 | MATH |
[
{
"content": "Let ABDEFGHIJKLM be a regular dodecagon with center C and circumradius 6. Let S be the circumcircle of polygon ABDEFGHIJKLM. Let Z be the line through points K and D. Let V be the midpoint of segment LG. Line Y is the reflection of line Z across point C. Circle R is the reflection of circle S acro... | 11.56 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center L and circumradius 11. Let Z be the circumcircle of polygon ABCDE. Let K be the perpendicular bisector of segment BL. Point R is the reflection of point C across line K. Point P is the inversion of point R with respect to circle Z. What is the length of segment... | 20.11 | MATH |
[
{
"content": "Let ABCDEFGIJKLM be a regular dodecagon with center H and circumradius 5. Let Z be the reflection of point G across point J. Point Y is the midpoint of segment MC. Point W is the midpoint of segment HY. What is the distance between points W and Z? Express your answer as a decimal number rounded to... | 9.28 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center M and circumradius 1. Point Q is the reflection of point E across segment BA. Let X be the reflection of point G across point C. Line V is the angle bisector of angle HEQ. Point O is the reflection of point H across line V. Let P be the midpoint of s... | 0.39 | MATH |
[
{
"content": "Let ABDE be a square with center C and circumradius 5. Line V passes through points E and D. Let T be the circumcircle of polygon ABDE. Let M be the reflection of circle T across line V. Point J is the inversion of point A with respect to circle M. What is the measure of angle AJE, in radians? Exp... | 0.79 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Z and circumradius 10. Let O be the reflection of point G across point J. Point U is the midpoint of segment JB. Point Y is the midpoint of segment HO. Find the length of segment UY. Express your answer as a decimal number rounded to 2 decimal pl... | 10.65 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center N and circumradius 11. Let M be the line through point E parallel to segment AD. Let V be the reflection of point G across point F. Point W is the reflection of point V across line M. What is the distance between points N and W? Express your answer as a de... | 12.75 | MATH |
[
{
"content": "Let ABCDEFGIJK be a regular 10-gon with center H and circumradius 10. Let U be the midpoint of segment EB. Let V be the perpendicular bisector of segment IE. Point P is the reflection of point D across point U. Point W is the reflection of point P across line V. What is the measure of angle JDW, i... | 0.31 | MATH |
[
{
"content": "ABCDEFGIJKLM is a regular dodecagon with center H and circumradius 10. Line Y is the perpendicular bisector of segment KF. Let W be the angle bisector of angle AHB. Let V be the reflection of line Y across line W. Line U passes through points A and D. Let N be the reflection of line U across line ... | 32.35 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center Z and circumradius 7. Let U be the line through points F and L. Let Y be the perpendicular bisector of segment EK. Let X be the reflection of line Y through point J. Line V is the reflection of line X across line U. Line M passes through point Z para... | 23.98 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center G and circumradius 9. Let U be the perpendicular bisector of segment EG. Point W lies on line U at distance 7 from point C. Line F passes through point B perpendicular to segment GE. Point T is the reflection of point W across segment GE. Point V is the ref... | 23.56 | MATH |
[
{
"content": "ABCD is a square with center R and circumradius 5. Line N is the angle bisector of angle ABC. Let F be the reflection of line N through point C. Let W be the line through points C and A. Point G is the intersection of lines F and W. Let X be the midpoint of segment GD. Find the distance between po... | 10.31 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center X and circumradius 1. Let Q be the reflection of point E across point A. Line N passes through points Q and H. Line S passes through point H perpendicular to line N. Point L is the reflection of point E across line S. What is the distance between point... | 2.43 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center Z and circumradius 2. Point X is the midpoint of segment AF. Line Y is the perpendicular bisector of segment CZ. Line N is the reflection of line Y across point X. Point U is the reflection of point E across line N. Find the length of segment UF. Express ... | 4.38 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center N and circumradius 9. Let Y be the line through points G and L. Point X is the intersection of line Y and segment IA. Point O is the reflection of point L across segment IA. What is the length of segment OX? Express your answer as a decimal numbe... | 4.66 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center T and circumradius 6. Let R be the midpoint of segment CA. Point Z is the midpoint of segment ER. Point J is the midpoint of segment BZ. What is the distance between points J and T? Express your answer as a decimal number rounded to 2 decimal places.\n\n... | 2.25 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center P and circumradius 5. Point W is the midpoint of segment GF. Line S is the perpendicular bisector of segment DW. Let Z be the line through point P perpendicular to line S. Point Y is the reflection of point F across line Z. Point X is the reflection of poin... | 9.27 | MATH |
[
{
"content": "ABCDEFHIJKL is a regular 11-gon with center G and circumradius 2. Let S be the circumcircle of polygon ABCDEFHIJKL. Let O be the angle bisector of angle KDL. Point T is the reflection of point A across line O. Let R be the reflection of circle S through point J. Let U be the inversion of point F i... | 2.17 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center N and circumradius 9. Let Z be the line through points N and A. Line X is the angle bisector of angle DEA. Let L be the reflection of line X across line Z. Point P is the reflection of point B across line L. What is the length of segment PG? Express yo... | 11.8 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center S and circumradius 4. Let R be the rotation of point F by angle pi/4 around point S. Point Q is the reflection of point B across point F. Let O be the line through points R and Q. Let N be the angle bisector of angle RSC. Let H be the reflection of line ... | 16.14 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center U and circumradius 11. Point K is the midpoint of segment EB. Segments KA and CJ intersect at point O. Find the distance between points K and O. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format... | 6.74 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center T and circumradius 8. Line M is the perpendicular bisector of segment AT. Let N be the reflection of point D across point F. Point V is obtained by rotating point T by angle 5pi/6 about point F. Line S passes through point N perpendicular to line M. Point L ... | 15.45 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center X and circumradius 1. Let R be the circumcircle of polygon ABCDEFGHI. Let M be the midpoint of segment HI. Point T is the inversion of point M with respect to circle R. What is the distance between points C and T? Express your answer as a decimal number rou... | 1.94 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center Y and circumradius 9. Line S is the angle bisector of angle YDC. Let U be the midpoint of segment AY. Let O be the reflection of line S through point F. Point Q is the reflection of point U across line O. Find the length of segment QG. Express your answer ... | 32.09 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center Q and circumradius 9. Point Y is obtained by rotating point J by angle pi/6 about point I. Let O be the angle bisector of angle GIY. Line M passes through point B perpendicular to line O. Let V be the reflection of line M through point L. Let N b... | 20.44 | MATH |
[
{
"content": "Let ABCDEFGI be a regular octagon with center H and circumradius 1. Line L passes through points I and H. Point V is the reflection of point I across point E. Let X be the perpendicular bisector of segment GE. Line W passes through point V perpendicular to line L. Line U is the reflection of line ... | 11.07 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center O and circumradius 9. Let L be the circumcircle of polygon ABCDEFGH. Point Z is the reflection of point O across point F. Let N be the inversion of point Z in circle L. Point M is the midpoint of segment OE. Point W is the midpoint of segment ME. Let K... | 3.32 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center M and circumradius 1. Point T is the midpoint of segment KB. Point W is the midpoint of segment DE. Line Q is the angle bisector of angle WTJ. Point P is the reflection of point I across line Q. What is the length of segment AP? Express your answer a... | 1.55 | MATH |
[
{
"content": "ABCDFGHIJKLM is a regular dodecagon with center E and circumradius 1. Point T is the midpoint of segment GI. Let W be the angle bisector of angle GEC. Line P is the angle bisector of angle BAG. Point Y is the reflection of point B across line P. Point Q is the reflection of point T across line W. ... | 0.39 | MATH |
[
{
"content": "ABCD is a square with center I and circumradius 12. Point J is obtained by rotating point D by angle pi/6 about point B. Let R be the line through points J and A. Line Z is the reflection of line R across point B. Point V is the reflection of point B across line R. Point Q is the reflection of poi... | 0.79 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center M and circumradius 8. Line O is the perpendicular bisector of segment ME. Point H is the midpoint of segment BM. Point G is the reflection of point H across line O. Find the distance between points G and M. Express your answer as a decimal number rounded to ... | 12.0 | MATH |
[
{
"content": "ABCDEG is a regular hexagon with center F and circumradius 1. Let T be the reflection of point E across point C. Let K be the reflection of point C across point B. Line M is the angle bisector of angle CEF. Point Z is the midpoint of segment AB. Point Y is the reflection of point Z across line M. ... | 3.79 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center M and circumradius 6. Let K be the rotation of point E by angle pi/12 around point C. Let X be the vector from point E to point B. Let Y be point C translated by vector X. Point I is the reflection of point K across point M. Let R be the line through p... | 15.41 | MATH |
[
{
"content": "Let ABCDEFGHIJKL be a regular dodecagon with center U and circumradius 12. Point Z is the midpoint of segment KF. Let P be the reflection of point I across point Z. Let R be the line through point P parallel to segment AG. Point X is the reflection of point J across line R. Let Y be the reflection... | 30.84 | MATH |
[
{
"content": "BCDEFGHIJKLM is a regular dodecagon with center A and circumradius 2. Let X be the perpendicular bisector of segment FA. Line Z is the reflection of line X across point F. Point U is the reflection of point G across line Z. Find the distance between points U and A. Express your answer as a decimal... | 4.38 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center O and circumradius 12. Point Y is the midpoint of segment ED. Let X be the angle bisector of angle HEC. Let N be the line through point Y parallel to line X. Point Q is the reflection of point O across line N. Find the length of segment JQ. Express y... | 18.77 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center X and circumradius 9. Let J be the reflection of point X across point C. Point G is the midpoint of segment DE. Let L be the midpoint of segment GE. What is the distance between points L and J? Express your answer as a decimal number rounded to 2 decimal... | 21.7 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center R and circumradius 2. Let N be the perpendicular bisector of segment DA. Line O passes through point C perpendicular to line N. Point H is the reflection of point R across line O. Line P is the angle bisector of angle RHD. Point Z is the reflection of point R a... | 1.31 | MATH |
[
{
"content": "ABCDEFGHIJKL is a regular dodecagon with center U and circumradius 5. Let S be the midpoint of segment IU. Let Z be the line through points C and J. Point Q is the midpoint of segment HD. Let V be the line through points Q and F. Let M be the reflection of line Z through point F. Lines V and M int... | 11.61 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center W and circumradius 4. Line G passes through point C perpendicular to segment AB. Let V be the circumcircle of polygon ABCDE. Circle K is the reflection of circle V across line G. Let T be the inversion of point B in circle K. Point N is the midpoint of segment ... | 6.39 | MATH |
[
{
"content": "Let VA = 8. BCDEFG is a regular hexagon with center A and circumradius 3. Line P is the angle bisector of angle AEB. Line Q is the reflection of line P across point C. Line J is the reflection of line Q across point G. Point H is the reflection of point F across line J. Find the distance between p... | 15.59 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center Y and circumradius 8. Let X be the midpoint of segment FA. Line I passes through point X parallel to segment GF. Point O lies on line I. Find the measure of angle OXA, in radians. Express your answer as a decimal number rounded to 2 decimal places.\n\nPre... | 2.69 | MATH |
[
{
"content": "ABCEFGHIJKLM is a regular dodecagon with center D and circumradius 2. Let X be the circumcircle of polygon ABCEFGHIJKLM. Circle R is the reflection of circle X across point M. Circle T is the reflection of circle R across point F. Point W is the inversion of point G with respect to circle T. What ... | 5.13 | MATH |
[
{
"content": "ABCDEGHIJK is a regular 10-gon with center F and circumradius 9. Let P be the perpendicular bisector of segment IE. Let L be the reflection of line P through point A. Point X is the reflection of point G across line L. Let M be the reflection of point G across point X. Let Z be the reflection of p... | 47.81 | MATH |
[
{
"content": "Let ABCDEFG be a regular 7-gon with center W and circumradius 3. Line M is the angle bisector of angle GDW. Let O be the line through points W and D. Line P is the reflection of line O across line M. Point T is the reflection of point C across line P. What is the distance between points B and T? E... | 6.63 | MATH |
[
{
"content": "Let ABCDEFGHIJK be a regular 11-gon with center R and circumradius 2. Let X be the midpoint of segment AD. Let S be the line through points I and D. Line T passes through point X parallel to line S. Point O is the reflection of point A across line T. Let N be the reflection of point O across point... | 1.77 | MATH |
[
{
"content": "Let ABCDEFGHIJ be a regular 10-gon with center V and circumradius 3. Let O be the circumcircle of polygon ABCDEFGHIJ. Let W be the reflection of circle O through point G. Circle P is the reflection of circle W across point V. Let L be the inversion of point D in circle P. Point R is the midpoint o... | 0.23 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center K and circumradius 9. Point T is the reflection of point K across segment AC. Line N passes through point T perpendicular to segment AC. Let I be the midpoint of segment KA. Point Y is the reflection of point I across segment AC. Point H is the reflection of po... | 9.0 | MATH |
[
{
"content": "ABCDEF is a regular hexagon with center H and circumradius 6. Let O be the angle bisector of angle BEC. Let Z be the rotation of point C by angle pi/4 around point F. Let G be the angle bisector of angle DZC. Line R is the reflection of line G across line O. Line L is the reflection of line O acro... | 20.82 | MATH |
[
{
"content": "ABCDEFGHI is a regular 9-gon with center M and circumradius 9. Let X be the midpoint of segment FM. Point T is the midpoint of segment AG. Let W be the midpoint of segment DT. Find the distance between points X and W. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent ... | 4.67 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center X and circumradius 1. Line M is the angle bisector of angle CBE. Let Y be the line through point A parallel to line M. Let Z be the reflection of line Y through point D. Point H is the reflection of point C across line Z. What is the distance between poi... | 2.65 | MATH |
[
{
"content": "Let ABCDE be a regular 5-gon with center Z and circumradius 10. Line X passes through points A and Z. Line X and segment DB intersect at point U. Point Q is the reflection of point C across segment DB. Let M be the reflection of point E across point B. Find the measure of angle UQM, in radians. Ex... | 1.26 | MATH |
[
{
"content": "ABCDE is a regular 5-gon with center S and circumradius 9. Point J is the midpoint of segment BE. Let O be the midpoint of segment JE. Point V is the midpoint of segment BO. Point Z is the reflection of point V across segment DB. What is the distance between points O and Z? Express your answer as ... | 12.45 | MATH |
[
{
"content": "Let ABCDEF be a regular hexagon with center I and circumradius 7. Let J be the perpendicular bisector of segment IA. Point R is the midpoint of segment BD. Line U passes through point I perpendicular to line J. Point M is the reflection of point R across line U. Find the distance between points E ... | 3.5 | MATH |
[
{
"content": "BCDEFGHIJK is a regular 10-gon with center A and circumradius 11. Let Z be the midpoint of segment KE. Let W be the line through points C and J. Let M be the line through point Z parallel to line W. Line S passes through point K parallel to line M. Point O is the reflection of point Z across segme... | 15.0 | MATH |
[
{
"content": "Let ABCDEFGHJKL be a regular 11-gon with center I and circumradius 1. Line S passes through points L and I. Point M is the reflection of point I across point J. Line O passes through point M perpendicular to line S. Point W is the reflection of point G across line O. What is the length of segment ... | 1.49 | MATH |
[
{
"content": "ABCDF is a regular 5-gon with center E and circumradius 11. Line H is the perpendicular bisector of segment ED. Point S is the midpoint of segment EB. Line Z passes through point D perpendicular to line H. Point Q is the reflection of point S across line Z. Find the length of segment EQ. Express y... | 5.5 | MATH |
[
{
"content": "Let ABCDEFGH be a regular octagon with center W and circumradius 5. Point U is the midpoint of segment GE. Point X is the reflection of point D across segment HU. Point Z is the reflection of point A across segment HU. What is the distance between points Z and X? Express your answer as a decimal n... | 9.24 | MATH |
[
{
"content": "ABCDEFGH is a regular octagon with center N and circumradius 7. Line O passes through points N and C. Let S be the midpoint of segment AB. Let L be the midpoint of segment GA. Point I is the reflection of point S across line O. What is the length of segment IL? Express your answer as a decimal num... | 11.2 | MATH |
[
{
"content": "ABCDEFGHJKLM is a regular dodecagon with center I and circumradius 11. Point T is the reflection of point K across point E. Point Q is the reflection of point A across segment BK. Let S be the perpendicular bisector of segment MH. Let N be the reflection of line S through point T. Line R passes th... | 37.24 | MATH |
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