messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
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[
{
"content": "Let YJ = 4. Let N be the reflection of point Y across point J. Line L is the perpendicular bisector of segment JY. Point O is obtained by rotating point N by angle pi/4 about point Y. Let D be the angle bisector of angle OJN. Let R be the line through point J parallel to line L. Point W is the ref... | 8.81 | MATH |
[
{
"content": "QZ = 12. Let U be the vector from point Z to point Q. Let P be point Q translated by vector U. Let J be the rotation of point Z by angle 11pi/12 around point Q. Let R be the reflection of point Z across point J. Point N is the reflection of point Q across segment RZ. Point I is the midpoint of seg... | 6.4 | MATH |
[
{
"content": "SX = 1. Point J is obtained by rotating point X by angle pi/12 about point S. Let H be the midpoint of segment SX. Point B is the reflection of point H across point J. Let F be the line through point B perpendicular to segment XJ. Point I is the reflection of point S across line F. What is the dis... | 1.12 | MATH |
[
{
"content": "Let FK = 12. Let E be the rotation of point K by angle pi/3 around point F. Let V be the midpoint of segment FE. Point J is the centroid of triangle FEK. Point N is the midpoint of segment JV. Point Y is the reflection of point K across point N. Point P is the reflection of point Y across segment ... | 17.32 | MATH |
[
{
"content": "NX = 8. Point E is obtained by rotating point N by angle 7pi/12 about point X. Let I be the angle bisector of angle NXE. Line F is the reflection of line I across point N. Point H is the reflection of point N across line F. Point J is the midpoint of segment HN. What is the inradius of triangle JH... | 0.78 | MATH |
[
{
"content": "Let XQ = 8. Let G be the rotation of point Q by angle 5pi/6 around point X. Point D is the reflection of point G across point Q. Let J be the circumcenter of triangle DQX. Point N is the incenter of triangle DQX. Point T is the midpoint of segment DQ. What is the inradius of triangle TNJ? Express ... | 0.11 | MATH |
[
{
"content": "GV = 2. Point A is obtained by rotating point V by angle pi/3 about point G. Let C be the reflection of point A across point G. Let D be the reflection of point G across point A. Point O is the reflection of point A across point V. What is the inradius of triangle COD? Express your answer as a dec... | 1.36 | MATH |
[
{
"content": "Let FC = 10. Let L be the rotation of point F by angle pi/3 around point C. Point T is the midpoint of segment LC. Point A is the circumcenter of triangle CFT. Let E be the midpoint of segment TA. Point R is the midpoint of segment TC. Find the measure of angle ERF, in radians. Express your answer... | 5.41 | MATH |
[
{
"content": "Let SC = 3. Point T is the midpoint of segment CS. Line E is the angle bisector of angle CTS. Line Y is the perpendicular bisector of segment CT. Point H lies on line Y at distance 10 from point S. Let F be the reflection of point T across point H. Let A be the reflection of line Y across line E. ... | 20.14 | MATH |
[
{
"content": "Let XK = 2. Point Z is obtained by rotating point K by angle pi/12 about point X. Let S be the perpendicular bisector of segment ZK. Point Y is the reflection of point K across point X. Let N be the line through point K parallel to line S. Let Q be the midpoint of segment YX. Point L is the reflec... | 0.37 | MATH |
[
{
"content": "RZ = 5. Let N be the midpoint of segment ZR. Let K be the midpoint of segment RN. Point Q is the midpoint of segment ZK. Point I is obtained by rotating point N by angle pi/6 about point Z. Point Y is obtained by rotating point Z by angle pi/4 about point R. Let J be the midpoint of segment QI. Li... | 2.74 | MATH |
[
{
"content": "Let YC = 5. Point J is the reflection of point C across point Y. Let F be the rotation of point Y by angle 7pi/12 around point C. Line G is the perpendicular bisector of segment JY. Let E be the centroid of triangle YCF. Point U is the orthocenter of triangle YCF. Point A is the reflection of poin... | 37.24 | MATH |
[
{
"content": "Let CZ = 1. Let D be the rotation of point Z by angle pi/12 around point C. Let W be the angle bisector of angle DZC. Point P is the reflection of point C across line W. Point Y is the reflection of point D across line W. Point J is on line W. Point G is the reflection of point J across segment ZD... | 1.12 | MATH |
[
{
"content": "ST = 1. Line D passes through points T and S. Point H is obtained by rotating point T by angle 5pi/12 about point S. Let A be the midpoint of segment SH. Point I is the reflection of point H across line D. Point O is the midpoint of segment TA. Let K be the reflection of line D through point I. Po... | 1.39 | MATH |
[
{
"content": "Let EV = 9. Point Y is obtained by rotating point E by angle 7pi/12 about point V. Circle F is the incircle of triangle EYV. Point R is the centroid of triangle EYV. Let S be the inversion of point Y in circle F. What is the distance between points S and R? Express your answer as a decimal number ... | 0.82 | MATH |
[
{
"content": "Let FO = 11. Point P is obtained by rotating point O by angle 11pi/12 about point F. Let B be the rotation of point F by angle pi/3 around point O. Line E is the perpendicular bisector of segment PF. Point T is the reflection of point B across line E. Point W is the midpoint of segment PO. Find th... | 0.66 | MATH |
[
{
"content": "CO = 3. Point B is obtained by rotating point O by angle pi/2 about point C. Let L be the incenter of triangle COB. Point M is the reflection of point C across segment OB. Point I is the reflection of point L across segment CO. Find the distance between points I and M. Express your answer as a dec... | 4.42 | MATH |
[
{
"content": "ZN = 8. Point R is obtained by rotating point N by angle pi/3 about point Z. Point K is the orthocenter of triangle RNZ. Let B be the midpoint of segment ZR. Let X be the midpoint of segment RB. What is the measure of angle XKN, in radians? Express your answer as a decimal number rounded to 2 deci... | 4.62 | MATH |
[
{
"content": "CD = 11. Point S is obtained by rotating point C by angle 3pi/4 about point D. Point R is the incenter of triangle DSC. Let Z be the midpoint of segment DS. Point L is the midpoint of segment ZR. Let K be the midpoint of segment ZS. Find the distance between points K and L. Express your answer as ... | 5.18 | MATH |
[
{
"content": "Let BM = 10. Let P be the rotation of point B by angle 11pi/12 around point M. Line Q passes through point P perpendicular to segment BM. Point U is obtained by rotating point P by angle 3pi/4 about point B. Point E is the reflection of point U across segment BM. Point G is the reflection of point... | 43.3 | MATH |
[
{
"content": "GJ = 10. Let N be the rotation of point J by angle 3pi/4 around point G. Let E be the reflection of point G across point N. Point U is the orthocenter of triangle JEN. Let R be the circumcenter of triangle JEN. Let B be the line through point R parallel to segment EN. Point Z is the intersection o... | 11.79 | MATH |
[
{
"content": "ER = 5. Point P is obtained by rotating point E by angle 7pi/12 about point R. Point C is the reflection of point P across point E. Point V is the incenter of triangle ECR. Point O is the midpoint of segment EC. Find the length of segment VO. Express your answer as a decimal number rounded to 2 de... | 3.77 | MATH |
[
{
"content": "RD = 8. Point M is obtained by rotating point D by angle pi/4 about point R. Let H be the rotation of point R by angle 3pi/4 around point D. Let O be the midpoint of segment RH. Point C is the circumcenter of triangle MRO. Point Z is the incenter of triangle MRO. Point W is the incenter of triangl... | 5.02 | MATH |
[
{
"content": "Let OK = 5. Point S is obtained by rotating point K by angle 3pi/4 about point O. Line M passes through point O perpendicular to segment SK. Let E be the reflection of point K across point O. Let Z be the circumcircle of triangle KOS. Let U be the rotation of point O by angle pi/3 around point E. ... | 11.79 | MATH |
[
{
"content": "EB = 4. Point J is the reflection of point B across point E. Let Y be the rotation of point J by angle 7pi/12 around point B. Point P is the midpoint of segment EY. Point Z is the circumcenter of triangle JPE. Let Q be the angle bisector of angle JZB. Point M is the midpoint of segment PE. Point D... | 5.6 | MATH |
[
{
"content": "Let DW = 3. Point R is obtained by rotating point W by angle pi/2 about point D. Let C be the perpendicular bisector of segment RD. Let A be the line through point W perpendicular to line C. Point U is obtained by rotating point D by angle pi/6 about point W. Let G be the circumcenter of triangle ... | 11.07 | MATH |
[
{
"content": "QJ = 2. Point P is obtained by rotating point Q by angle 3pi/4 about point J. Let C be the circumcenter of triangle QJP. Point I is the midpoint of segment PQ. Let W be the midpoint of segment CP. Find the length of segment IW. Express your answer as a decimal number rounded to 2 decimal places.\n... | 0.93 | MATH |
[
{
"content": "SD = 10. Point P is obtained by rotating point S by angle 11pi/12 about point D. Let X be the midpoint of segment PS. Point O is the midpoint of segment PD. Let J be the reflection of point X across point O. Let L be the midpoint of segment PO. Find the measure of angle LJX, in radians. Express yo... | 3.24 | MATH |
[
{
"content": "Let RB = 2. Let K be the rotation of point B by angle pi/4 around point R. Let E be the reflection of point R across point B. Point W is the orthocenter of triangle KRE. Let L be the centroid of triangle KRE. What is the distance between points W and L? Express your answer as a decimal number roun... | 2.15 | MATH |
[
{
"content": "Let OC = 4. Point Q is obtained by rotating point O by angle 11pi/12 about point C. Point E is the midpoint of segment QO. Let K be the incircle of triangle CEO. Point N is the inversion of point E with respect to circle K. Find the distance between points Q and N. Express your answer as a decimal... | 4.09 | MATH |
[
{
"content": "WY = 11. Line D is the perpendicular bisector of segment WY. Line H passes through point W perpendicular to line D. Point K is obtained by rotating point W by angle pi/12 about point Y. Point I is obtained by rotating point W by angle pi/12 about point K. Let B be the midpoint of segment IW. Let N... | 0.19 | MATH |
[
{
"content": "EP = 11. Point T is obtained by rotating point E by angle 11pi/12 about point P. Point J is the centroid of triangle PTE. Line O passes through point E parallel to segment PT. Point A is the reflection of point J across line O. Find the distance between points E and A. Express your answer as a dec... | 10.92 | MATH |
[
{
"content": "Let UW = 11. Let H be the rotation of point W by angle 2pi/3 around point U. Point M is the incenter of triangle WUH. Let T be the orthocenter of triangle WUH. Point B is the reflection of point M across segment UH. Point O is the reflection of point T across point B. Find the distance between poi... | 9.53 | MATH |
[
{
"content": "AK = 7. Point I is obtained by rotating point A by angle pi/2 about point K. Circle Y is the circumcircle of triangle AIK. Let R be the circumcenter of triangle AIK. Circle N is the reflection of circle Y across point R. Let S be the reflection of point K across point I. Let F be the inversion of ... | 14.6 | MATH |
[
{
"content": "YS = 4. Point N is the midpoint of segment YS. Let T be the line through point S perpendicular to segment SY. Point V is obtained by rotating point N by angle 5pi/6 about point S. Line A passes through point N parallel to line T. Point O is the reflection of point V across line A. Point I is the m... | 5.62 | MATH |
[
{
"content": "Let XJ = 9. Point B is obtained by rotating point J by angle 7pi/12 about point X. Let U be the reflection of point B across point J. Point T is the orthocenter of triangle BUX. Point O is the circumcenter of triangle BUX. Point A is the reflection of point U across segment TO. Let D be the midpoi... | 0.76 | MATH |
[
{
"content": "Let DH = 9. Point Y is obtained by rotating point H by angle pi/6 about point D. Point V is obtained by rotating point H by angle pi/2 about point Y. Let R be the rotation of point Y by angle 5pi/6 around point H. Let T be the line through points H and Y. Line J is the perpendicular bisector of se... | 6.14 | MATH |
[
{
"content": "PQ = 9. Point K is the midpoint of segment PQ. Let A be the perpendicular bisector of segment KP. Point J lies on line A at distance 8 from point Q. Point R is the midpoint of segment QJ. Point E is the reflection of point K across point J. Let S be the reflection of point R across point P. What i... | 3.76 | MATH |
[
{
"content": "Let OQ = 4. Let H be the vector from point O to point Q. Let M be the perpendicular bisector of segment OQ. Let J be the line through point O perpendicular to line M. Let U be the rotation of point O by angle pi/6 around point Q. Let L be the reflection of point U across point O. Point X is obtain... | 0.64 | MATH |
[
{
"content": "TA = 5. Point Y is the midpoint of segment TA. Point M is the midpoint of segment AY. Let B be the rotation of point Y by angle pi/2 around point T. Point W is the reflection of point T across point M. Point H is the midpoint of segment WB. Point D is the reflection of point A across point H. Find... | 8.84 | MATH |
[
{
"content": "Let DL = 1. Let H be the rotation of point D by angle pi/2 around point L. Let K be the midpoint of segment DH. Let S be the reflection of point L across point H. Line F passes through points D and K. Let X be the reflection of line F through point L. Point Y is the reflection of point S across po... | 5.0 | MATH |
[
{
"content": "VG = 5. Let X be the rotation of point G by angle 11pi/12 around point V. Let Y be the line through point G perpendicular to segment VX. Point N is the reflection of point V across line Y. Point F is the orthocenter of triangle VXG. Find the length of segment NF. Express your answer as a decimal n... | 37.0 | MATH |
[
{
"content": "Let TK = 10. Point E is the reflection of point K across point T. Let C be the rotation of point T by angle 2pi/3 around point E. Point F is the orthocenter of triangle KEC. Let Q be the line through point E parallel to segment CK. Let N be the reflection of point K across point E. Point Z is the ... | 15.28 | MATH |
[
{
"content": "Let QA = 5. Point K is obtained by rotating point Q by angle 5pi/12 about point A. Let Y be the reflection of point A across point Q. Let B be the line through point Q perpendicular to segment QK. Point T is the reflection of point A across line B. Point W is the midpoint of segment QY. Point C is... | 2.5 | MATH |
[
{
"content": "OF = 10. Let L be the rotation of point O by angle pi/3 around point F. Let V be the circumcircle of triangle OLF. Let Y be the centroid of triangle OLF. Let E be the angle bisector of angle YFO. Let X be the reflection of line E through point L. Circle G is the reflection of circle V across line ... | 2.39 | MATH |
[
{
"content": "BE = 8. Point Z is obtained by rotating point E by angle 3pi/4 about point B. Let Q be the incircle of triangle ZBE. Point R is the orthocenter of triangle ZBE. Point J is the inversion of point R with respect to circle Q. What is the length of segment ZJ? Express your answer as a decimal number r... | 7.56 | MATH |
[
{
"content": "Let IW = 8. Let L be the rotation of point I by angle 3pi/4 around point W. Let F be the rotation of point L by angle pi/2 around point W. Line R passes through points W and F. Let C be the line through point L parallel to line R. Let O be the reflection of point L across point F. Point M is the r... | 241.14 | MATH |
[
{
"content": "Let PU = 1. Let Z be the rotation of point P by angle 3pi/4 around point U. Let G be the midpoint of segment PU. Let S be the reflection of point Z across point U. Point O is the midpoint of segment PG. Find the circumradius of triangle SZO. Express your answer as a decimal number rounded to 2 dec... | 1.08 | MATH |
[
{
"content": "Let JZ = 7. Let G be the reflection of point Z across point J. Let U be the line through point G perpendicular to segment JZ. Line I is the perpendicular bisector of segment GZ. Let X be the midpoint of segment JZ. Let W be the reflection of line I across line U. Let M be the reflection of line W ... | 101.45 | MATH |
[
{
"content": "UR = 4. Let X be the rotation of point R by angle pi/4 around point U. Let F be the perpendicular bisector of segment UX. Line O passes through point R parallel to line F. Let I be the centroid of triangle RUX. Point K is the reflection of point X across line O. What is the distance between points... | 1.13 | MATH |
[
{
"content": "GF = 10. Let S be the rotation of point F by angle pi/6 around point G. Let D be the orthocenter of triangle GSF. Point N is the reflection of point D across segment FG. Let U be the midpoint of segment NF. What is the length of segment UD? Express your answer as a decimal number rounded to 2 deci... | 3.54 | MATH |
[
{
"content": "IB = 4. Let E be the rotation of point I by angle pi around point B. Point P is obtained by rotating point I by angle 5pi/6 about point E. Let L be the midpoint of segment PE. Let V be the midpoint of segment LI. Point Y is the reflection of point L across point B. Let S be the line through points... | 0.85 | MATH |
[
{
"content": "HA = 10. Point K is obtained by rotating point H by angle 11pi/12 about point A. Let P be the perpendicular bisector of segment AK. Let L be the angle bisector of angle AKH. Point T is the reflection of point H across line P. Point M is the reflection of point A across line L. Let B be the incircl... | 4.91 | MATH |
[
{
"content": "XB = 11. Point Y is the reflection of point B across point X. Let I be the midpoint of segment XY. Let F be the midpoint of segment IY. Point Z is obtained by rotating point F by angle 5pi/6 about point X. Point K is the reflection of point Z across point X. Point G is the reflection of point X ac... | 36.84 | MATH |
[
{
"content": "YK = 9. Let L be the rotation of point K by angle pi/6 around point Y. Point F is the incenter of triangle LKY. Line H passes through point F parallel to segment YL. Point E is the intersection of segment KY and line H. What is the measure of angle FEK, in radians? Express your answer as a decimal... | 0.52 | MATH |
[
{
"content": "Let KI = 1. Let E be the rotation of point K by angle 5pi/6 around point I. Let Z be the midpoint of segment EI. Point Q is the reflection of point E across point K. Point B is the centroid of triangle KEI. What is the measure of angle ZBQ, in radians? Express your answer as a decimal number round... | 0.04 | MATH |
[
{
"content": "ON = 5. Point L is obtained by rotating point O by angle pi/12 about point N. Point Y is obtained by rotating point L by angle 5pi/6 about point N. Point Q is the reflection of point L across point N. Point C is the centroid of triangle LNY. Point X is the reflection of point Q across segment YL. ... | 5.47 | MATH |
[
{
"content": "LM = 1. Let P be the rotation of point M by angle 11pi/12 around point L. Circle W is the incircle of triangle LPM. Point B is the inversion of point L with respect to circle W. Let E be the midpoint of segment BP. Let Q be the centroid of triangle LPM. Find the length of segment EQ. Express your ... | 0.5 | MATH |
[
{
"content": "VS = 2. Let I be the rotation of point S by angle 5pi/6 around point V. Point G is the reflection of point I across point V. Point Z is the reflection of point I across segment SG. Point P is the incenter of triangle GIS. What is the measure of angle PZG, in radians? Express your answer as a decim... | 1.36 | MATH |
[
{
"content": "Let UW = 11. Let A be the rotation of point W by angle pi/12 around point U. Let X be the midpoint of segment WU. Point L is obtained by rotating point U by angle 2pi/3 about point A. Point S is obtained by rotating point W by angle pi about point L. Point E is the reflection of point S across poi... | 1.28 | MATH |
[
{
"content": "Let Y be the perpendicular bisector of segment BB. Let U be the reflection of point B across point B. Let I be the reflection of point B across point U. Point O is the reflection of point I across line Y. What is the distance between points B and O? Express your answer as a decimal number rounded ... | 2.0 | MATH |
[
{
"content": "DB = 11. Let C be the rotation of point B by angle 5pi/6 around point D. Point S is the centroid of triangle BDC. Let Y be the midpoint of segment BD. Point V is the midpoint of segment BY. Point M is the reflection of point S across segment CB. Segments CB and SM intersect at point Q. What is the... | 8.0 | MATH |
[
{
"content": "JD = 2. Let P be the rotation of point D by angle pi/2 around point J. Let A be the rotation of point P by angle pi/4 around point D. Point V is the midpoint of segment JP. Let X be the reflection of point D across point P. Let O be the line through point P parallel to segment AX. Point Z is the m... | 0.09 | MATH |
[
{
"content": "Let AF = 8. Point K is obtained by rotating point A by angle pi/3 about point F. Let X be the perpendicular bisector of segment AF. Line S is the reflection of line X across point F. Point E is the reflection of point K across line S. Point Y is the circumcenter of triangle EFK. Find the length of... | 7.06 | MATH |
[
{
"content": "HA = 2. Point X is obtained by rotating point A by angle pi/4 about point H. Let J be the reflection of point A across point X. Point P is obtained by rotating point X by angle 3pi/4 about point A. Let U be the orthocenter of triangle JXH. Let D be the line through point J parallel to segment XH. ... | 3.25 | MATH |
[
{
"content": "Let FP = 4. Let R be the rotation of point F by angle 5pi/12 around point P. Point U is the midpoint of segment PR. Point S is the orthocenter of triangle PRF. Let G be the centroid of triangle PRF. Point M is the reflection of point U across point G. Find the length of segment SM. Express your an... | 1.81 | MATH |
[
{
"content": "Let OY = 6. Line D is the perpendicular bisector of segment YO. Point A is the midpoint of segment YO. Point P lies on line D at distance 4 from point O. Let R be the perpendicular bisector of segment AP. Point M is the reflection of point O across line R. Point F is the reflection of point M acro... | 2.14 | MATH |
[
{
"content": "Let XK = 10. Let Q be the midpoint of segment KX. Let R be the midpoint of segment QX. Let T be the rotation of point R by angle 3pi/4 around point Q. Let P be the rotation of point K by angle 3pi/4 around point R. Point O is the midpoint of segment TX. Point U is the reflection of point Q across ... | 0.44 | MATH |
[
{
"content": "XW = 7. Point U is obtained by rotating point W by angle pi about point X. Let S be the rotation of point W by angle 5pi/6 around point U. Let Q be the reflection of point X across point S. Point Y is the reflection of point Q across point W. Point T is the midpoint of segment WS. Let H be the mid... | 190.28 | MATH |
[
{
"content": "Let ZS = 6. Let X be the rotation of point Z by angle pi/3 around point S. Let D be the circumcircle of triangle ZXS. Point H is the midpoint of segment ZX. Point A is the inversion of point H with respect to circle D. Point C is the midpoint of segment SZ. What is the measure of angle XAC, in rad... | 15.59 | MATH |
[
{
"content": "Let OS = 1. Let W be the rotation of point S by angle 2pi/3 around point O. Point U is obtained by rotating point S by angle pi/4 about point O. Let N be the midpoint of segment WS. Let E be the rotation of point S by angle 7pi/12 around point U. Point K is the reflection of point U across point E... | 0.02 | MATH |
[
{
"content": "Let BE = 9. Point S is obtained by rotating point B by angle pi/12 about point E. Point F is obtained by rotating point E by angle 7pi/12 about point B. Let X be the centroid of triangle BES. Circle Z is the circumcircle of triangle BES. Let L be the inversion of point F in circle Z. Point O is th... | 2.41 | MATH |
[
{
"content": "Let XB = 2. Let S be the midpoint of segment XB. Let E be the rotation of point B by angle 5pi/6 around point X. Let U be the line through points B and E. Point H is the reflection of point S across line U. Let C be the angle bisector of angle EHS. Point I is the reflection of point X across line ... | 0.25 | MATH |
[
{
"content": "Let QL = 8. Point I is the midpoint of segment LQ. Point S is the midpoint of segment LI. Line D is the perpendicular bisector of segment LS. Point W is the reflection of point I across line D. Point V is obtained by rotating point L by angle pi/3 about point S. Let B be the reflection of point V ... | 2.29 | MATH |
[
{
"content": "JT = 9. Point M is obtained by rotating point T by angle 5pi/6 about point J. Let R be the reflection of point T across point M. Let V be the rotation of point M by angle pi/3 around point R. Let E be the line through points J and R. Line P passes through point V parallel to segment MJ. Point U is... | 80.42 | MATH |
[
{
"content": "HX = 10. Let P be the rotation of point X by angle 2pi/3 around point H. Point R is the midpoint of segment PX. Let Q be the midpoint of segment XH. Point E is the orthocenter of triangle RHQ. Find the distance between points P and E. Express your answer as a decimal number rounded to 2 decimal pl... | 10.41 | MATH |
[
{
"content": "Let DG = 10. Point W is obtained by rotating point G by angle pi/2 about point D. Point U is the reflection of point D across segment WG. Point S is obtained by rotating point G by angle pi/4 about point U. Point R is the reflection of point S across segment WG. Let N be the reflection of point G ... | 182.84 | MATH |
[
{
"content": "Let VL = 1. Point C is obtained by rotating point L by angle 11pi/12 about point V. Point R lies on segment VL. Let A be the reflection of point R across point L. Let F be the midpoint of segment VL. Point P is the midpoint of segment CF. Line U passes through point P parallel to segment VL. Point... | 0.25 | MATH |
[
{
"content": "Point S is the midpoint of segment D52H. Let V be the circumcircle of triangle H. Circle O is the reflection of circle V across point H. Let G be the reflection of circle O through point R. Let U be the inversion of point H in circle G. Point F is the reflection of point H across segment HN. Point... | 0.67 | MATH |
[
{
"content": "Let AX = 6. Let T be the rotation of point A by angle 5pi/12 around point X. Let U be the reflection of point A across point T. Let B be the orthocenter of triangle TUX. Point M is the midpoint of segment BT. Let Q be the centroid of triangle TUX. Find the measure of angle MXQ, in radians. Express... | 18.93 | MATH |
[
{
"content": "KZ = 2. Point O is obtained by rotating point K by angle pi/4 about point Z. Let X be the rotation of point Z by angle 5pi/6 around point K. Let A be the midpoint of segment XO. Let U be the perpendicular bisector of segment ZO. Point Q is on line U. Point B lies on line U at distance 4 from point... | 0.91 | MATH |
[
{
"content": "Let XP = 5. Let W be the rotation of point P by angle pi/12 around point X. Let C be the midpoint of segment PW. Let Y be the rotation of point P by angle 2pi/3 around point C. Point Z is the reflection of point Y across segment WP. Let U be the incircle of triangle WPX. Let K be the inversion of ... | 0.77 | MATH |
[
{
"content": "Let GW = 2. Let J be the rotation of point G by angle pi around point W. Point F is obtained by rotating point J by angle pi/4 about point W. Let M be the rotation of point J by angle 2pi/3 around point W. Point V is the reflection of point J across point M. Point Q is the midpoint of segment GW. ... | 1.46 | MATH |
[
{
"content": "MQ = 1. Point L is the midpoint of segment MQ. Point P is obtained by rotating point L by angle pi/2 about point M. Point A is obtained by rotating point M by angle 5pi/12 about point P. Point U is the reflection of point M across point P. Line D is the perpendicular bisector of segment UA. Point ... | 0.07 | MATH |
[
{
"content": "Let JS = 3. Let L be the rotation of point S by angle 7pi/12 around point J. Let U be the rotation of point J by angle pi/4 around point S. Point X is the reflection of point U across point J. Point M is the incenter of triangle LSU. Line P is the perpendicular bisector of segment LS. Point R is t... | 0.97 | MATH |
[
{
"content": "VE = 3. Point T is the reflection of point E across point V. Let N be the rotation of point E by angle pi/12 around point V. Point W is obtained by rotating point N by angle pi/6 about point T. Point U is the centroid of triangle VWT. Point J is the midpoint of segment TU. Let B be the orthocenter... | 3.3 | MATH |
[
{
"content": "BH = 4. Line L passes through points B and H. Let F be the rotation of point H by angle 5pi/12 around point B. Point P is the reflection of point F across line L. Let E be the angle bisector of angle FPH. Line U is the reflection of line E across line L. Point R is the reflection of point H across... | 0.18 | MATH |
[
{
"content": "Let OH = 10. Line L passes through points O and H. Point G is obtained by rotating point O by angle pi/12 about point H. Let C be the line through points O and G. Let K be the reflection of point H across point O. Let R be the midpoint of segment GH. Let A be the line through point G perpendicular... | 78.53 | MATH |
[
{
"content": "ZF = 8. Let N be the midpoint of segment FZ. Point K is obtained by rotating point F by angle 7pi/12 about point N. Point U is obtained by rotating point F by angle 2pi/3 about point K. Point C is the reflection of point U across point N. Point Q is the reflection of point Z across segment UC. Poi... | 27.69 | MATH |
[
{
"content": "Let WG = 7. Let D be the rotation of point G by angle 3pi/4 around point W. Let X be the midpoint of segment WD. Point M is the reflection of point W across segment DG. Let O be the circumcenter of triangle DGX. Find the length of segment OM. Express your answer as a decimal number rounded to 2 de... | 3.31 | MATH |
[
{
"content": "XJ = 1. Let Z be the rotation of point J by angle pi/4 around point X. Point R is the centroid of triangle JXZ. Line G passes through point J parallel to segment XZ. Let V be the midpoint of segment XZ. Point S is the reflection of point V across line G. Find the measure of angle RVS, in radians. ... | 0.05 | MATH |
[
{
"content": "Let VJ = 11. Point X is obtained by rotating point V by angle 3pi/4 about point J. Let S be the reflection of point J across point X. Let W be the incircle of triangle JVS. Point Y is the inversion of point X with respect to circle W. Find the length of segment YV. Express your answer as a decimal... | 10.93 | MATH |
[
{
"content": "Let ZN = 5. Line B passes through points Z and N. Point J is obtained by rotating point Z by angle 5pi/12 about point N. Let H be the midpoint of segment NZ. Line K passes through point J parallel to line B. Point R is the reflection of point H across line K. Let W be the midpoint of segment ZR. L... | 0.79 | MATH |
[
{
"content": "VD = 11. Let R be the reflection of point V across point D. Let X be the perpendicular bisector of segment RV. Point W lies on line X at distance 9 from point V. Line K passes through points W and R. Line G is the reflection of line K across point D. Let A be the reflection of line K across line G... | 355.81 | MATH |
[
{
"content": "MJ = 5. Point U is obtained by rotating point M by angle pi/2 about point J. Let Y be the line through point M perpendicular to segment MJ. Let C be the rotation of point J by angle pi/4 around point M. Let Q be the angle bisector of angle JCM. Line T is the reflection of line Y across line Q. Poi... | 5.96 | MATH |
[
{
"content": "Let BR = 6. Point Q is the midpoint of segment BR. Point V is obtained by rotating point Q by angle 2pi/3 about point R. Let C be the rotation of point R by angle pi/6 around point V. Point D is the midpoint of segment QR. Let T be the rotation of point B by angle 5pi/12 around point D. Line I is ... | 7.16 | MATH |
[
{
"content": "XO = 9. Point M is the midpoint of segment OX. Line B is the perpendicular bisector of segment MO. Point R is the reflection of point X across line B. Point Z is on line B with |ZX| = 5. Point L is the reflection of point X across point Z. Let P be the midpoint of segment RL. Let Y be the reflecti... | 7.7 | MATH |
[
{
"content": "Let NB = 5. Let V be the rotation of point N by angle pi/4 around point B. Point A is obtained by rotating point N by angle 5pi/6 about point V. Let K be the line through point N parallel to segment AB. Point X is the reflection of point B across line K. Point O is the orthocenter of triangle VAB.... | 5.96 | MATH |
[
{
"content": "Let DL = 5. Let K be the reflection of point L across point D. Let Y be the reflection of point D across point L. Let Q be the rotation of point D by angle pi/6 around point Y. Line S is the perpendicular bisector of segment KQ. Point A is the reflection of point L across line S. Let W be the circ... | 6.55 | MATH |
[
{
"content": "NA = 11. Point G is obtained by rotating point N by angle pi/3 about point A. Point T is obtained by rotating point G by angle 11pi/12 about point N. Let I be the reflection of point G across point N. Point B is the reflection of point A across segment TI. What is the circumradius of triangle IBA?... | 15.65 | MATH |
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