messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
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[
{
"content": "Let AJ = 1. Point Z is the midpoint of segment JA. Point Q is obtained by rotating point J by angle 3pi/4 about point Z. Point F is the midpoint of segment ZQ. Let W be the midpoint of segment QA. Let U be the angle bisector of angle JWQ. Point I is the reflection of point Q across line U. Find th... | 0.0 | MATH |
[
{
"content": "GN = 8. Let P be the midpoint of segment NG. Let Z be the rotation of point P by angle pi/2 around point G. Let W be the reflection of point P across point Z. Point D is the reflection of point P across point N. Point I is the reflection of point D across segment PW. Find the distance between poin... | 17.89 | MATH |
[
{
"content": "Let BY = 8. Point P is obtained by rotating point Y by angle pi/6 about point B. Point E is obtained by rotating point Y by angle 3pi/4 about point P. Line W is the angle bisector of angle BPY. Let R be the midpoint of segment BY. Point A is the midpoint of segment RY. Point D is the reflection of... | 0.29 | MATH |
[
{
"content": "TF = 11. Point W is obtained by rotating point F by angle 5pi/6 about point T. Point B is the midpoint of segment FW. Point G is the reflection of point F across point T. Let M be the centroid of triangle FBT. Find the distance between points M and G. Express your answer as a decimal number rounde... | 14.94 | MATH |
[
{
"content": "PY = 6. Let D be the rotation of point Y by angle 5pi/6 around point P. Point G is the reflection of point D across point P. Point E is the reflection of point Y across point P. Let U be the midpoint of segment YG. Let W be the reflection of point G across point D. Find the circumradius of triangl... | 20.2 | MATH |
[
{
"content": "Let AV = 12. Let B be the midpoint of segment VA. Let Y be the rotation of point B by angle 5pi/6 around point A. Circle X is the incircle of triangle BYV. Let O be the midpoint of segment YV. Point G is the inversion of point O with respect to circle X. What is the distance between points O and G... | 2.75 | MATH |
[
{
"content": "Let RJ = 4. Point E is obtained by rotating point R by angle 7pi/12 about point J. Let Q be the incenter of triangle EJR. Let S be the midpoint of segment RQ. Let B be the midpoint of segment JR. What is the distance between points S and B? Express your answer as a decimal number rounded to 2 deci... | 0.68 | MATH |
[
{
"content": "ME = 12. Point Q is obtained by rotating point E by angle 5pi/12 about point M. Point X is the midpoint of segment QM. Let T be the reflection of point E across point X. Let I be the midpoint of segment QT. Point P is the midpoint of segment QI. What is the circumradius of triangle PMI? Express yo... | 5.97 | MATH |
[
{
"content": "WR = 4. Point P is the midpoint of segment RW. Let L be the line through points W and P. Point X is obtained by rotating point P by angle 3pi/4 about point R. Line Y is the perpendicular bisector of segment WX. Line E passes through point R parallel to line Y. Let Z be the reflection of line L thr... | 3.21 | MATH |
[
{
"content": "SI = 2. Point R is obtained by rotating point I by angle pi/3 about point S. Let D be the orthocenter of triangle SRI. Line F is the angle bisector of angle DIS. Point Q is the reflection of point R across line F. Find the length of segment QS. Express your answer as a decimal number rounded to 2 ... | 1.04 | MATH |
[
{
"content": "BM = 2. Let F be the rotation of point B by angle pi/6 around point M. Point T is the midpoint of segment MB. Line R is the perpendicular bisector of segment BT. Point O is the reflection of point F across line R. Let I be the midpoint of segment MF. What is the measure of angle TIO, in radians? E... | 0.13 | MATH |
[
{
"content": "Let SV = 7. Point F is obtained by rotating point S by angle 3pi/4 about point V. Point B is the reflection of point V across segment FS. Point Y is obtained by rotating point F by angle pi/2 about point B. Line K passes through point Y parallel to segment FS. Point C is the circumcenter of triang... | 9.7 | MATH |
[
{
"content": "UY = 4. Let O be the rotation of point Y by angle 11pi/12 around point U. Let X be the reflection of point U across point Y. Point S is the reflection of point U across segment OX. Let H be the midpoint of segment XY. Find the distance between points H and S. Express your answer as a decimal numbe... | 6.04 | MATH |
[
{
"content": "Let UZ = 4. Let W be the rotation of point U by angle 7pi/12 around point Z. Point R is obtained by rotating point W by angle 3pi/4 about point U. Let F be the midpoint of segment UZ. Line D is the angle bisector of angle URF. Let M be the line through point W parallel to line D. Point K is the re... | 6.97 | MATH |
[
{
"content": "XF = 5. Point U is obtained by rotating point X by angle pi/12 about point F. Point L is the midpoint of segment XF. Point P is the reflection of point L across segment XU. Point S is the midpoint of segment PU. Point K is the reflection of point P across segment UF. What is the measure of angle X... | 0.92 | MATH |
[
{
"content": "Let OA = 6. Let D be the rotation of point A by angle pi/3 around point O. Point X is obtained by rotating point O by angle pi/3 about point A. Point H is the reflection of point D across point O. Let V be the reflection of point O across point H. Let R be the reflection of point H across point A.... | 0.59 | MATH |
[
{
"content": "Let FG = 12. Point A is obtained by rotating point G by angle 3pi/4 about point F. Let Q be the orthocenter of triangle AGF. Point P is the circumcenter of triangle AGF. Line X passes through point P parallel to segment GF. Point L is the reflection of point A across line X. Point D is the reflect... | 180.85 | MATH |
[
{
"content": "DK = 7. Point X is the midpoint of segment KD. Line P is the perpendicular bisector of segment DK. Point U is obtained by rotating point X by angle 5pi/6 about point D. Let M be the reflection of line P through point D. Let F be the reflection of line P through point U. Point J is obtained by rota... | 2.86 | MATH |
[
{
"content": "Let PZ = 12. Point T is obtained by rotating point P by angle 2pi/3 about point Z. Point U is the midpoint of segment ZP. Let W be the midpoint of segment PT. Line N is the perpendicular bisector of segment WU. Point R is the reflection of point P across line N. Find the distance between points U ... | 10.39 | MATH |
[
{
"content": "Let GP = 8. Let I be the midpoint of segment GP. Let D be the rotation of point P by angle 2pi/3 around point I. Line B is the perpendicular bisector of segment PD. Point F is the reflection of point G across line B. Point C is the reflection of point D across segment IP. What is the distance betw... | 4.0 | MATH |
[
{
"content": "Let KY = 11. Point Z is obtained by rotating point Y by angle 7pi/12 about point K. Point F is the reflection of point Z across segment YK. Let G be the incenter of triangle YKZ. Let J be the reflection of point G across point F. Find the measure of angle JZF, in radians. Express your answer as a ... | 54.4 | MATH |
[
{
"content": "Let RZ = 11. Let S be the rotation of point Z by angle 5pi/12 around point R. Circle V is the circumcircle of triangle ZRS. Point P is the midpoint of segment RS. Point B is the inversion of point P with respect to circle V. Find the distance between points S and B. Express your answer as a decima... | 9.03 | MATH |
[
{
"content": "Let PN = 7. Let E be the rotation of point N by angle pi/4 around point P. Point G is the incenter of triangle PEN. Point M is the reflection of point G across segment NP. Let Z be the orthocenter of triangle PEN. Find the distance between points M and Z. Express your answer as a decimal number ro... | 3.89 | MATH |
[
{
"content": "Let OJ = 9. Let Q be the rotation of point O by angle pi/3 around point J. Point F is the midpoint of segment JO. Let N be the rotation of point J by angle pi/3 around point F. Let H be the rotation of point F by angle pi/2 around point J. Let E be the angle bisector of angle QJH. Let L be the cen... | 17.54 | MATH |
[
{
"content": "LB = 4. Let S be the rotation of point L by angle 3pi/4 around point B. Let E be the centroid of triangle SLB. Point X is the incenter of triangle SLB. Let K be the midpoint of segment EX. What is the length of segment KL? Express your answer as a decimal number rounded to 2 decimal places.\n\nPre... | 3.75 | MATH |
[
{
"content": "PW = 3. Let Z be the midpoint of segment WP. Let A be the rotation of point Z by angle pi/12 around point W. Let I be the midpoint of segment AP. Point V is the centroid of triangle PWA. Point B is the reflection of point V across segment PW. Find the length of segment BI. Express your answer as a... | 0.81 | MATH |
[
{
"content": "Let DN = 4. Let V be the rotation of point N by angle pi/12 around point D. Let M be the rotation of point D by angle 5pi/12 around point V. Point K is the orthocenter of triangle NVM. Let C be the reflection of point N across point K. Point Y is the midpoint of segment VM. Let I be the circumcent... | 7.2 | MATH |
[
{
"content": "BU = 12. Point F is obtained by rotating point B by angle 5pi/6 about point U. Point J is the circumcenter of triangle FUB. Let Z be the incenter of triangle FUB. What is the circumradius of triangle JZB? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in... | 5.87 | MATH |
[
{
"content": "TH = 4. Let J be the reflection of point H across point T. Let Q be the rotation of point H by angle 7pi/12 around point J. Let A be the midpoint of segment TQ. Line P is the angle bisector of angle AHT. Point C is the midpoint of segment QH. Point W is the reflection of point J across line P. Poi... | 1.99 | MATH |
[
{
"content": "Let RJ = 3. Let M be the perpendicular bisector of segment JR. Let C be the rotation of point J by angle 2pi/3 around point R. Let U be the reflection of line M through point C. Let H be the centroid of triangle JCR. Point A is the reflection of point R across line U. What is the length of segment... | 9.54 | MATH |
[
{
"content": "RO = 5. Let W be the rotation of point R by angle 3pi/4 around point O. Line U is the perpendicular bisector of segment RW. Line Y is the perpendicular bisector of segment WO. Let A be the line through point O perpendicular to line U. Line X is the reflection of line Y across line A. Line X and se... | 3.23 | MATH |
[
{
"content": "Let TQ = 8. Let G be the midpoint of segment QT. Point C is obtained by rotating point G by angle 11pi/12 about point T. Line Z is the angle bisector of angle GCQ. Point Y is the reflection of point T across line Z. Line B is the angle bisector of angle CGY. Point F is the reflection of point C ac... | 1.41 | MATH |
[
{
"content": "TG = 1. Point J is obtained by rotating point G by angle pi/12 about point T. Let B be the midpoint of segment GT. Line I is the angle bisector of angle JGT. Point U is the reflection of point B across line I. What is the inradius of triangle UGB? Express your answer as a decimal number rounded to... | 0.15 | MATH |
[
{
"content": "Let CA = 9. Point K is obtained by rotating point C by angle pi/6 about point A. Point F is obtained by rotating point A by angle pi/2 about point K. Point W is the circumcenter of triangle KAF. Point L is the midpoint of segment FC. Point P is the midpoint of segment LF. What is the length of seg... | 5.57 | MATH |
[
{
"content": "Let LM = 2. Point Z is the midpoint of segment ML. Let R be the rotation of point L by angle pi/3 around point Z. Line N is the perpendicular bisector of segment ZM. Line X passes through point Z parallel to line N. Point C is the reflection of point R across line X. What is the inradius of triang... | 0.29 | MATH |
[
{
"content": "Let KM = 5. Point O is obtained by rotating point M by angle 3pi/4 about point K. Circle T is the incircle of triangle MKO. Point P is the inversion of point K with respect to circle T. Point W is the circumcenter of triangle MKO. What is the distance between points P and W? Express your answer as... | 1.13 | MATH |
[
{
"content": "CN = 4. Let L be the midpoint of segment CN. Point P is obtained by rotating point L by angle 11pi/12 about point N. Let R be the rotation of point P by angle pi/3 around point L. Let U be the midpoint of segment RL. Point O is the midpoint of segment NU. Point V is the midpoint of segment ON. Poi... | 0.59 | MATH |
[
{
"content": "Let WT = 8. Point V is the reflection of point T across point W. Point S is the reflection of point V across point T. Point Y is obtained by rotating point T by angle pi/4 about point W. Line R passes through points S and T. Line P is the reflection of line R across point Y. Line L is the reflecti... | 245.02 | MATH |
[
{
"content": "Let H be the reflection of point J across point F. Point G is the centroid of triangle J. Let D be the reflection of point H across point G. Let I be the midpoint of segment JS. Find the distance between points I and D. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresen... | 1.76 | MATH |
[
{
"content": "Let GV = 1. Point M is obtained by rotating point V by angle pi/2 about point G. Let K be the reflection of point V across point M. Let F be the reflection of point M across point V. Let R be the midpoint of segment VG. Line J is the perpendicular bisector of segment VG. Point L is the reflection ... | 2.25 | MATH |
[
{
"content": "NW = 6. Point S is the midpoint of segment WN. Point T is obtained by rotating point W by angle pi/12 about point S. Line G is the perpendicular bisector of segment SN. Line A is the reflection of line G across point S. Point L is the reflection of point T across line G. Point Q is the reflection ... | 5.74 | MATH |
[
{
"content": "LU = 1. Point R is obtained by rotating point L by angle pi/12 about point U. Point Q is the midpoint of segment LU. Point F is the midpoint of segment UQ. Let I be the midpoint of segment RF. Point M is the reflection of point L across segment RF. What is the measure of angle UMI, in radians? Exp... | 0.09 | MATH |
[
{
"content": "WE = 3. Point P is obtained by rotating point E by angle 5pi/12 about point W. Point Z is the reflection of point P across point W. Let V be the rotation of point P by angle pi/4 around point Z. Point F is the midpoint of segment EP. Line D passes through points V and F. Let R be the centroid of t... | 6.18 | MATH |
[
{
"content": "JW = 4. Point K is obtained by rotating point J by angle 7pi/12 about point W. Let D be the rotation of point K by angle pi around point W. Point I is the reflection of point J across point K. Let N be the line through points I and J. Point G is the reflection of point W across line N. Let E be th... | 23.18 | MATH |
[
{
"content": "Let XO = 2. Point G is the reflection of point O across point X. Point H is obtained by rotating point G by angle pi/3 about point O. Let E be the midpoint of segment HG. Point S is the midpoint of segment XH. Point L is the reflection of point S across segment HO. What is the distance between poi... | 2.65 | MATH |
[
{
"content": "BV = 3. Point Y is the reflection of point V across point B. Point P is obtained by rotating point V by angle 2pi/3 about point Y. Point N is the midpoint of segment VB. Let M be the reflection of point P across point B. Point Q is obtained by rotating point B by angle 7pi/12 about point M. Let K ... | 7.66 | MATH |
[
{
"content": "XY = 6. Point R is obtained by rotating point X by angle 5pi/12 about point Y. Let Z be the rotation of point R by angle pi/3 around point Y. Point B is the reflection of point R across segment YX. Point S is the reflection of point X across point R. Let L be the line through points S and Y. Point... | 0.1 | MATH |
[
{
"content": "TI = 12. Point S is obtained by rotating point T by angle pi/12 about point I. Let K be the angle bisector of angle ITS. Point Z is the reflection of point S across line K. Point A is the centroid of triangle IZS. Find the distance between points A and Z. Express your answer as a decimal number ro... | 2.29 | MATH |
[
{
"content": "Let DJ = 7. Point T is the reflection of point J across point D. DB = 10. Let F be the reflection of point D across point T. Let X be the midpoint of segment BD. Let Z be the midpoint of segment BT. Point Q is the reflection of point Z across segment BD. Find the length of segment XQ. Express your... | 3.5 | MATH |
[
{
"content": "ZK = 12. Point Y is obtained by rotating point Z by angle 3pi/4 about point K. Point L is the midpoint of segment ZK. Point J is the reflection of point Z across point Y. Let D be the line through point J parallel to segment LZ. Let W be the reflection of point Z across point J. Let R be the refle... | 3968.11 | MATH |
[
{
"content": "VH = 6. Point X is the reflection of point H across point V. Point U is obtained by rotating point H by angle pi/3 about point X. Let W be the rotation of point H by angle pi/2 around point U. Let J be the reflection of point X across point W. Line Z is the angle bisector of angle UHJ. Point C is ... | 42.69 | MATH |
[
{
"content": "Let WB = 9. Point Z is the reflection of point W across point B. Point M is obtained by rotating point Z by angle pi/12 about point W. Point G is the midpoint of segment MW. Point Y is the midpoint of segment ZM. What is the circumradius of triangle GBY? Express your answer as a decimal number rou... | 4.54 | MATH |
[
{
"content": "Let LX = 3. Let C be the rotation of point L by angle pi/3 around point X. Let H be the midpoint of segment CL. Point M is the circumcenter of triangle HXC. Circle Y is the incircle of triangle HXC. Let R be the inversion of point H in circle Y. What is the inradius of triangle MXR? Express your a... | 0.14 | MATH |
[
{
"content": "PC = 2. Let U be the rotation of point P by angle pi/3 around point C. Let E be the midpoint of segment PU. Let Z be the angle bisector of angle UEC. Point M is the reflection of point C across line Z. Let T be the incenter of triangle CPU. Let I be the midpoint of segment PT. Let V be the reflect... | 4.06 | MATH |
[
{
"content": "CF = 2. Let S be the rotation of point F by angle 3pi/4 around point C. Point N is the reflection of point S across point C. Let R be the centroid of triangle NFC. Point D is the reflection of point R across segment CN. Find the length of segment DN. Express your answer as a decimal number rounded... | 0.98 | MATH |
[
{
"content": "Let IW = 4. Point C is the midpoint of segment WI. Point V is obtained by rotating point C by angle 7pi/12 about point I. Point X is the reflection of point V across segment IW. Let R be the incenter of triangle IWV. Let B be the midpoint of segment CR. Find the inradius of triangle XWB. Express y... | 0.65 | MATH |
[
{
"content": "SE = 8. Point K is obtained by rotating point S by angle 2pi/3 about point E. Let B be the angle bisector of angle EKS. Point A is the midpoint of segment KE. Point N is the midpoint of segment AE. Point D is the midpoint of segment SA. Point Y is the reflection of point D across line B. Find the ... | 7.13 | MATH |
[
{
"content": "Let WF = 4. Let S be the rotation of point F by angle 5pi/12 around point W. Point R is obtained by rotating point W by angle 3pi/4 about point S. Let D be the midpoint of segment WF. Point B is the reflection of point W across segment RD. Point T is the orthocenter of triangle RDS. Point C is the... | 3.26 | MATH |
[
{
"content": "JC = 9. Let Q be the rotation of point J by angle pi/6 around point C. Point D is the incenter of triangle CJQ. Point Y is the reflection of point D across point J. Point V is the reflection of point Y across segment CJ. Let O be the reflection of point V across point Q. What is the measure of ang... | 37.05 | MATH |
[
{
"content": "Let VE = 1. Point X is obtained by rotating point V by angle pi/6 about point E. Point A is the reflection of point X across point E. Point B is the midpoint of segment VX. Let S be the reflection of point V across point A. Line U passes through point B perpendicular to segment VX. Point Q is the ... | 0.24 | MATH |
[
{
"content": "Let K be the orthocenter of triangle O. Point Q is the midpoint of segment IK. Point D is the reflection of point I across segment PW36. Let J be the midpoint of segment DQ. Find the distance between points J and I. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent th... | 0.52 | MATH |
[
{
"content": "TY = 9. Point C is obtained by rotating point T by angle 2pi/3 about point Y. Let J be the incenter of triangle CYT. Point U is the orthocenter of triangle CYT. Let Q be the midpoint of segment CU. Let I be the reflection of point Q across point J. Find the distance between points T and I. Express... | 4.67 | MATH |
[
{
"content": "Let UW = 1. Let T be the midpoint of segment WU. Let I be the perpendicular bisector of segment TW. Let G be the reflection of line I through point W. Point X is on line G with |XT| = 11. Point K is the reflection of point X across line I. Let A be the midpoint of segment UT. Let F be the incenter... | 1.31 | MATH |
[
{
"content": "Let AR = 10. Let N be the rotation of point A by angle pi/12 around point R. Let T be the rotation of point A by angle pi/2 around point R. Let V be the perpendicular bisector of segment NR. Let O be the incircle of triangle RNA. Circle W is the reflection of circle O across line V. Let H be the m... | 22.8 | MATH |
[
{
"content": "NH = 1. Point W is obtained by rotating point H by angle 5pi/12 about point N. Let P be the rotation of point N by angle 5pi/12 around point H. Let J be the incenter of triangle PNW. Let B be the incircle of triangle PNW. Point U is the inversion of point H with respect to circle B. Let R be the m... | 0.03 | MATH |
[
{
"content": "Let VM = 12. Let D be the rotation of point V by angle pi/6 around point M. Point S is the reflection of point D across point V. Point N is the orthocenter of triangle MSV. Point B is the midpoint of segment SM. Point Y is the midpoint of segment BV. Find the measure of angle YBN, in radians. Expr... | 3.53 | MATH |
[
{
"content": "Let MQ = 11. Point Z is obtained by rotating point Q by angle pi/6 about point M. Let T be the circumcenter of triangle ZQM. Let G be the angle bisector of angle TQZ. Point S is the reflection of point M across segment ZQ. Point O is the reflection of point S across line G. Find the length of segm... | 15.08 | MATH |
[
{
"content": "LZ = 3. Point M is obtained by rotating point Z by angle 7pi/12 about point L. Let C be the orthocenter of triangle ZLM. Let Q be the vector from point Z to point C. Point S is the translation of point M by vector Q. Point F is the midpoint of segment SM. Let J be the incenter of triangle ZLM. Cir... | 7.08 | MATH |
[
{
"content": "IL = 11. Line V passes through point I perpendicular to segment LI. Point Q is the reflection of point L across line V. Point C lies on line V at distance 5 from point L. Point B is the reflection of point C across point Q. Point W is the reflection of point C across point I. Let Y be the midpoint... | 6.04 | MATH |
[
{
"content": "Let WN = 11. Let K be the rotation of point N by angle 5pi/12 around point W. Let S be the line through points N and K. Let F be the line through point W perpendicular to line S. Let A be the midpoint of segment NK. Line R is the reflection of line F across point K. Point M is the reflection of po... | 30.25 | MATH |
[
{
"content": "HC = 11. Let S be the rotation of point H by angle 3pi/4 around point C. Point J is obtained by rotating point H by angle 5pi/12 about point S. Point M is the reflection of point H across segment CS. Let K be the circumcenter of triangle CJH. Let A be the midpoint of segment CJ. Point L is the mid... | 21.29 | MATH |
[
{
"content": "Let TP = 7. Line C is the perpendicular bisector of segment PT. Let L be the reflection of line C through point P. Point D is on line L with |DT| = 7. Point M is the reflection of point D across point P. Point V is the reflection of point P across segment TM. Point Y is the midpoint of segment DT.... | 13.12 | MATH |
[
{
"content": "LV = 7. Point G is obtained by rotating point L by angle pi/12 about point V. Point X is obtained by rotating point L by angle pi/3 about point V. Let P be the reflection of point X across point L. Let F be the line through point G parallel to segment VX. Line Q passes through point X perpendicula... | 9.3 | MATH |
[
{
"content": "Let TK = 9. Let S be the reflection of point K across point T. Let X be the vector from point T to point K. Point B is obtained by rotating point K by angle 11pi/12 about point T. Point G is obtained by rotating point K by angle 5pi/12 about point S. Point W is the translation of point G by vector... | 31.09 | MATH |
[
{
"content": "DJ = 9. Let A be the rotation of point J by angle pi/12 around point D. Point I is the reflection of point D across point J. Point M lies on segment JD. Point P is the reflection of point M across segment DA. Find the measure of angle IDP, in radians. Express your answer as a decimal number rounde... | 0.52 | MATH |
[
{
"content": "ZB = 7. Point L is obtained by rotating point B by angle 11pi/12 about point Z. Let X be the circumcircle of triangle ZBL. Let Q be the incenter of triangle ZBL. Let Y be the centroid of triangle ZBL. Point J is the reflection of point Y across segment ZB. Let G be the inversion of point J in circ... | 0.19 | MATH |
[
{
"content": "QW = 7. Let O be the perpendicular bisector of segment WQ. Line P is the reflection of line O across point W. Point J is the reflection of point Q across line P. Point T lies on line P at distance 1 from point J. Point A is the circumcenter of triangle QTW. Point G is the incenter of triangle QTW.... | 58.33 | MATH |
[
{
"content": "Let ZR = 2. Let O be the midpoint of segment ZR. Point Y is the reflection of point O across point R. Let W be the rotation of point Y by angle pi/4 around point Z. Point L is obtained by rotating point O by angle pi/3 about point Z. Point K is the midpoint of segment WY. Let P be the reflection o... | 0.2 | MATH |
[
{
"content": "Let VJ = 4. Let B be the reflection of point J across point V. Let Z be the rotation of point B by angle 5pi/6 around point J. Let Q be the line through points B and Z. Point G is the reflection of point V across point J. Line W passes through point V parallel to line Q. Let X be the midpoint of s... | 3.87 | MATH |
[
{
"content": "Let OZ = 8. Point Q is the midpoint of segment OZ. Point W is obtained by rotating point Z by angle 5pi/6 about point O. Let K be the midpoint of segment WQ. Line A is the perpendicular bisector of segment KQ. Line F is the perpendicular bisector of segment ZQ. Let J be the rotation of point Z by ... | 0.93 | MATH |
[
{
"content": "XI = 12. Let T be the midpoint of segment IX. Point D is obtained by rotating point T by angle 11pi/12 about point X. Point H is the midpoint of segment DT. Line J is the angle bisector of angle IHX. Point M is the reflection of point T across line J. Let Y be the centroid of triangle HMI. Find th... | 10.19 | MATH |
[
{
"content": "UO = 6. Let A be the rotation of point O by angle pi/2 around point U. Let E be the rotation of point A by angle 5pi/12 around point U. Let J be the midpoint of segment OU. Point X is the incenter of triangle UAO. Point K is the reflection of point X across segment EA. Find the measure of angle KJ... | 0.37 | MATH |
[
{
"content": "Let PT = 7. Let S be the midpoint of segment TP. Point X is the midpoint of segment PS. Point K is the reflection of point S across point P. Point Q is obtained by rotating point K by angle 3pi/4 about point X. Let Z be the reflection of point Q across point X. Point A is the reflection of point P... | 22.41 | MATH |
[
{
"content": "TV = 8. Point R is obtained by rotating point V by angle pi/2 about point T. Point Y is the midpoint of segment TR. Point C is the reflection of point V across point Y. Point A is the reflection of point C across segment RV. What is the measure of angle TAC, in radians? Express your answer as a de... | 0.79 | MATH |
[
{
"content": "Let XO = 10. Point P is obtained by rotating point X by angle pi/2 about point O. Let W be the line through points O and P. Point G is the reflection of point X across line W. Let L be the midpoint of segment OG. Let T be the reflection of point G across point P. What is the measure of angle PLT, ... | 25.0 | MATH |
[
{
"content": "Let ON = 7. Let E be the rotation of point O by angle 3pi/4 around point N. Point K is the midpoint of segment NE. Let T be the rotation of point K by angle pi/3 around point N. Point Q is the reflection of point T across point O. Line H is the perpendicular bisector of segment TQ. Point W is the ... | 12.93 | MATH |
[
{
"content": "YW = 4. YP = 4. Let U be the perpendicular bisector of segment PW. Let S be the reflection of point Y across point W. Point N is the reflection of point S across line U. Let G be the midpoint of segment PY. Find the distance between points N and G. Express your answer as a decimal number rounded t... | 6.0 | MATH |
[
{
"content": "YU = 3. Point O is obtained by rotating point Y by angle pi/4 about point U. Let H be the midpoint of segment YO. Point J is the orthocenter of triangle OUY. Let G be the midpoint of segment YH. What is the distance between points J and G? Express your answer as a decimal number rounded to 2 decim... | 0.75 | MATH |
[
{
"content": "WF = 7. Let J be the rotation of point F by angle 11pi/12 around point W. Point Z is the reflection of point J across segment WF. Point S is the circumcenter of triangle WJZ. Let O be the midpoint of segment ZS. Let U be the incenter of triangle WJZ. Find the distance between points U and O. Expre... | 0.94 | MATH |
[
{
"content": "Let CT = 8. Point S is obtained by rotating point T by angle pi/4 about point C. Point Y is the midpoint of segment CS. Point V is the reflection of point T across segment CS. Let G be the reflection of point V across point Y. Let I be the circumcenter of triangle TVG. Find the distance between po... | 7.62 | MATH |
[
{
"content": "YH = 9. Point A is the midpoint of segment HY. Point X is obtained by rotating point A by angle 5pi/6 about point H. Point T is the reflection of point X across point A. Line I is the angle bisector of angle ATH. Point N is the reflection of point Y across line I. Point W is the midpoint of segmen... | 8.86 | MATH |
[
{
"content": "YF = 1. Point J is the midpoint of segment FY. Let W be the rotation of point Y by angle 2pi/3 around point F. Point L is the reflection of point F across point W. Let B be the midpoint of segment JF. Let K be the reflection of point Y across point B. Find the circumradius of triangle LKJ. Express... | 1.19 | MATH |
[
{
"content": "YO = 7. Point B is obtained by rotating point O by angle 5pi/12 about point Y. Point V is the midpoint of segment BY. Let K be the reflection of point B across point O. Find the circumradius of triangle KOV. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer... | 19.04 | MATH |
[
{
"content": "Let ZI = 3. Let U be the reflection of point Z across point I. Let M be the rotation of point U by angle 11pi/12 around point I. Let N be the incenter of triangle IMZ. Let J be the circumcenter of triangle IMZ. Point Q is the reflection of point N across segment MZ. Point G is the reflection of po... | 1.49 | MATH |
[
{
"content": "Let BW = 3. Line F passes through points B and W. Point Q is obtained by rotating point B by angle 3pi/4 about point W. Let R be the rotation of point B by angle 5pi/12 around point Q. Point A is the reflection of point R across line F. Point P is the reflection of point Q across point R. Line M i... | 67.84 | MATH |
[
{
"content": "Let UI = 12. Let G be the rotation of point U by angle 11pi/12 around point I. Let F be the line through points G and I. Let Q be the reflection of point G across point I. Point W is the reflection of point U across line F. What is the inradius of triangle WUQ? Express your answer as a decimal num... | 0.2 | MATH |
[
{
"content": "Let XK = 2. Point Q is obtained by rotating point X by angle 11pi/12 about point K. Point E is the midpoint of segment QK. Let V be the centroid of triangle XQK. Point G is the reflection of point E across segment KX. What is the length of segment GV? Express your answer as a decimal number rounde... | 1.08 | MATH |
[
{
"content": "Let RO = 2. Point P is obtained by rotating point R by angle pi/2 about point O. Let H be the incenter of triangle RPO. Circle L is the incircle of triangle RPO. Point W is the inversion of point R with respect to circle L. Let J be the midpoint of segment HP. Find the length of segment JW. Expres... | 0.94 | MATH |
[
{
"content": "OV = 3. Point G is obtained by rotating point O by angle pi/2 about point V. Let F be the reflection of point G across point V. Let T be the circumcenter of triangle GOF. Let W be the line through points F and T. Let C be the circumcircle of triangle GOF. Let N be the rotation of point T by angle ... | 5.91 | MATH |
[
{
"content": "ZW = 9. Let E be the rotation of point W by angle 3pi/4 around point Z. Let T be the perpendicular bisector of segment WE. Point G is the midpoint of segment EZ. Point Q is the reflection of point G across line T. Point N is the orthocenter of triangle WEZ. Find the distance between points Q and N... | 18.82 | MATH |
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