messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
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[
{
"content": "XD = 2. Point O is obtained by rotating point X by angle 11pi/12 about point D. Let V be the midpoint of segment DO. Point T is the reflection of point V across segment XD. Let Q be the reflection of point T across point D. What is the inradius of triangle DQV? Express your answer as a decimal num... | 0.13 | MATH |
[
{
"content": "JQ = 9. Let D be the rotation of point Q by angle pi/12 around point J. Let S be the angle bisector of angle JQD. Point K is the midpoint of segment DQ. Point G is obtained by rotating point J by angle pi/12 about point D. Let C be the orthocenter of triangle JQD. Point P is the reflection of poin... | 0.19 | MATH |
[
{
"content": "Let ZH = 10. Let A be the rotation of point Z by angle 11pi/12 around point H. Point L is the orthocenter of triangle ZHA. Let W be the midpoint of segment ZH. Point Q is the centroid of triangle ZHA. Circle S is the incircle of triangle ZHA. Point D is the midpoint of segment WL. Let C be the inv... | 39.37 | MATH |
[
{
"content": "PZ = 10. Let U be the reflection of point Z across point P. Let O be the rotation of point U by angle pi/2 around point Z. Line A passes through points O and U. Let N be the line through point U perpendicular to line A. Let T be the line through point P perpendicular to line N. Let X be the reflec... | 6.16 | MATH |
[
{
"content": "YD = 6. Let T be the line through points Y and D. Let R be the midpoint of segment DY. Point V is obtained by rotating point R by angle 5pi/6 about point Y. Point G is the midpoint of segment YV. Let K be the midpoint of segment YR. Line W is the perpendicular bisector of segment GD. Line A is the... | 3.25 | MATH |
[
{
"content": "Line E passes through point F parallel to segment VI14. Point N is on line E with |NJ| = 1. Point C is obtained by rotating point J by angle 7pi/12 about point S. Point K is the reflection of point S across segment CV. Point H is the midpoint of segment SS. Let R be the midpoint of segment KH. Wha... | 1.16 | MATH |
[
{
"content": "Let TY = 10. Point U is obtained by rotating point T by angle 3pi/4 about point Y. Point A is the midpoint of segment UY. Let K be the centroid of triangle YTU. Point E is the reflection of point A across point K. What is the length of segment UE? Express your answer as a decimal number rounded to... | 13.87 | MATH |
[
{
"content": "Let RV = 2. Let J be the reflection of point R across point V. Let S be the rotation of point V by angle pi/2 around point J. Point U is the reflection of point V across point S. Point A is the circumcenter of triangle SUR. Point K is the reflection of point J across segment SU. What is the measur... | 1.33 | MATH |
[
{
"content": "GR = 1. Let E be the rotation of point R by angle pi/12 around point G. Point N is the midpoint of segment ER. Let M be the line through point E perpendicular to segment GE. Line J is the perpendicular bisector of segment GN. Let L be the midpoint of segment GE. Let A be the line through point R p... | 5.38 | MATH |
[
{
"content": "IV = 6. Let X be the rotation of point V by angle pi/12 around point I. Let Q be the midpoint of segment VI. Let U be the reflection of point V across point X. Point B is the midpoint of segment QU. Circle D is the circumcircle of triangle BVU. Let T be the inversion of point I in circle D. Let L ... | 3.36 | MATH |
[
{
"content": "Let PL = 1. Let U be the vector from point L to point P. Point R is the translation of point P by vector U. Let I be the rotation of point P by angle pi/6 around point R. Point A is the orthocenter of triangle PLI. Circle O is the circumcircle of triangle PLI. Let N be the inversion of point R in ... | 0.74 | MATH |
[
{
"content": "Let YB = 5. Point D is obtained by rotating point Y by angle 11pi/12 about point B. Let I be the angle bisector of angle YBD. Line M is the reflection of line I across point Y. Let T be the midpoint of segment BD. Point A is the reflection of point Y across line M. Let F be the circumcircle of tri... | 17.41 | MATH |
[
{
"content": "Let KW = 8. Let R be the midpoint of segment KW. Point Q is obtained by rotating point W by angle 7pi/12 about point R. Point L is the midpoint of segment KQ. Let I be the incenter of triangle QWK. What is the inradius of triangle LIR? Express your answer as a decimal number rounded to 2 decimal p... | 0.39 | MATH |
[
{
"content": "PL = 5. Point F is the reflection of point P across point L. Let M be the rotation of point L by angle pi/3 around point F. Let Y be the reflection of point P across point F. Point V is the midpoint of segment LF. Let W be the circumcircle of triangle FML. Let N be the inversion of point Y in circ... | 0.85 | MATH |
[
{
"content": "Let PZ = 3. Line Y is the perpendicular bisector of segment ZP. Point T lies on line Y at distance 2 from point Z. Point J is the midpoint of segment PZ. Point V is the reflection of point J across point T. Let I be the perpendicular bisector of segment ZV. Let W be the reflection of line I across... | 2.84 | MATH |
[
{
"content": "Let NY = 9. Let U be the rotation of point Y by angle 5pi/12 around point N. Let K be the reflection of point N across point Y. Let C be the reflection of point K across point N. Let V be the midpoint of segment UY. Let F be the midpoint of segment CV. What is the circumradius of triangle FKV? Exp... | 24.4 | MATH |
[
{
"content": "RF = 7. Let S be the rotation of point R by angle 5pi/6 around point F. Point I is the reflection of point S across segment FR. Let H be the angle bisector of angle ISF. Point M is the midpoint of segment FR. Point C is the reflection of point M across line H. Let B be the midpoint of segment CF. ... | 2.24 | MATH |
[
{
"content": "Let LY = 11. Let D be the rotation of point Y by angle pi/12 around point L. Let F be the rotation of point L by angle pi/4 around point D. Line N is the angle bisector of angle YLF. Line W is the reflection of line N across point D. Point P is the centroid of triangle LYD. Point I is the reflecti... | 25.69 | MATH |
[
{
"content": "Let WV = 3. Point Q is the reflection of point W across point V. Let K be the midpoint of segment QV. Point F is obtained by rotating point K by angle pi/4 about point Q. Point U is the midpoint of segment FK. Let R be the line through point U perpendicular to segment FW. Point N is the reflection... | 0.74 | MATH |
[
{
"content": "Let IQ = 6. Point V is obtained by rotating point I by angle pi/3 about point Q. Circle W is the incircle of triangle VQI. Let O be the midpoint of segment QI. Point A is the inversion of point I with respect to circle W. Line U is the perpendicular bisector of segment IA. Point C is the reflectio... | 1.05 | MATH |
[
{
"content": "NR = 2. Let V be the reflection of point R across point N. Let S be the rotation of point R by angle 11pi/12 around point V. Let D be the line through points V and S. Line H is the angle bisector of angle VNS. Let K be the rotation of point R by angle pi/4 around point S. Point E is the reflection... | 0.93 | MATH |
[
{
"content": "FS = 11. Point L is obtained by rotating point S by angle 7pi/12 about point F. Point B is the reflection of point S across point F. Let K be the reflection of point S across point L. Point T is the incenter of triangle FBL. What is the length of segment TK? Express your answer as a decimal number... | 21.81 | MATH |
[
{
"content": "QP = 6. Let N be the rotation of point P by angle 3pi/4 around point Q. Let E be the reflection of point Q across point N. Let J be the midpoint of segment PQ. Line I is the perpendicular bisector of segment NE. Point M is the reflection of point J across line I. Find the inradius of triangle NME.... | 0.44 | MATH |
[
{
"content": "AR = 8. Point U is the reflection of point R across point A. Let C be the rotation of point R by angle pi/12 around point A. Circle F is the circumcircle of triangle ACR. Let G be the reflection of point R across point U. Point S is the midpoint of segment CR. Let Q be the inversion of point S in ... | 32.16 | MATH |
[
{
"content": "BP = 1. Point K is obtained by rotating point B by angle 7pi/12 about point P. Let H be the rotation of point P by angle pi/4 around point B. Let J be the circumcircle of triangle BHP. Point S is the inversion of point K with respect to circle J. Let L be the incenter of triangle BHP. What is the ... | 0.22 | MATH |
[
{
"content": "Let PG = 8. Point I is obtained by rotating point P by angle pi/4 about point G. Let N be the incenter of triangle IGP. Line S passes through point I perpendicular to segment IG. Point J is the reflection of point N across line S. Point K is the reflection of point P across point J. What is the me... | 6.26 | MATH |
[
{
"content": "SQ = 4. Point B is obtained by rotating point S by angle pi/2 about point Q. Let C be the vector from point B to point Q. Point J is the reflection of point S across point B. Let M be point S translated by vector C. Line H is the angle bisector of angle QMJ. Point E is the centroid of triangle BQS... | 17.47 | MATH |
[
{
"content": "Let TI = 1. Let V be the reflection of point I across point T. Let P be the rotation of point T by angle pi/4 around point I. Point K is the reflection of point P across point V. Let H be the circumcenter of triangle KIP. Let R be the reflection of point K across point H. Find the length of segmen... | 2.08 | MATH |
[
{
"content": "DG = 10. Let N be the rotation of point G by angle pi/2 around point D. Let I be the midpoint of segment DG. Let T be the rotation of point D by angle pi/4 around point I. Line Z is the perpendicular bisector of segment TN. Point J is the reflection of point G across line Z. Let S be the line thro... | 17.54 | MATH |
[
{
"content": "RU = 6. Let T be the rotation of point U by angle 7pi/12 around point R. Let L be the rotation of point T by angle pi around point R. Let O be the perpendicular bisector of segment UR. Point Y is the circumcenter of triangle UTL. Line F is the reflection of line O across point L. Point X is the re... | 3.79 | MATH |
[
{
"content": "VY = 9. Point K is obtained by rotating point Y by angle pi/12 about point V. Let H be the midpoint of segment VY. Let C be the rotation of point K by angle pi/4 around point H. Point T is the midpoint of segment VC. Circle M is the incircle of triangle YVC. Let I be the circumcenter of triangle Y... | 4.67 | MATH |
[
{
"content": "MU = 3. Let Z be the rotation of point M by angle pi/6 around point U. Point J is the reflection of point Z across point U. Point Y is the orthocenter of triangle UZM. Circle S is the circumcircle of triangle UZM. Line B passes through point Z perpendicular to segment UZ. Let A be the line through... | 2.05 | MATH |
[
{
"content": "SB = 1. Line H passes through points B and S. Let C be the rotation of point B by angle 5pi/12 around point S. Point F is the midpoint of segment SB. Let K be the line through points C and F. Point W is the reflection of point B across line K. Point A is the reflection of point C across line H. Le... | 0.12 | MATH |
[
{
"content": "DG = 5. Let N be the rotation of point G by angle pi/3 around point D. Let W be the midpoint of segment DG. Point M is the reflection of point W across point G. Circle S is the incircle of triangle GND. Let A be the inversion of point N in circle S. What is the length of segment AM? Express your a... | 5.45 | MATH |
[
{
"content": "Let TE = 7. Point A is obtained by rotating point T by angle 5pi/12 about point E. Point J is the reflection of point A across point T. Point B is obtained by rotating point J by angle pi/6 about point T. Point C is the midpoint of segment EJ. Point U is the orthocenter of triangle JTE. Point Z is... | 8.39 | MATH |
[
{
"content": "TB = 3. Point C is obtained by rotating point B by angle 2pi/3 about point T. Line J is the angle bisector of angle TBC. Let O be the reflection of point C across point T. Point H is on line J with |HB| = 4. Point I is the reflection of point T across line J. Let G be the line through point I perp... | 0.6 | MATH |
[
{
"content": "RJ = 3. Point D is obtained by rotating point R by angle pi/3 about point J. Point Z is the midpoint of segment RJ. Let N be the rotation of point D by angle 11pi/12 around point J. Line S passes through points D and N. Let T be the line through points Z and N. Let X be the reflection of line S ac... | 0.41 | MATH |
[
{
"content": "RY = 2. Line I passes through point R perpendicular to segment YR. Point O is on line I with |OY| = 9. Line L passes through point Y parallel to line I. Point W is the reflection of point R across line L. Let S be the reflection of point O across point Y. Point B is on line L. Find the measure of ... | 9.0 | MATH |
[
{
"content": "KP = 11. Let Y be the midpoint of segment PK. Let Q be the rotation of point K by angle 7pi/12 around point Y. Let S be the midpoint of segment PQ. Point I is the reflection of point S across point P. Point L is the reflection of point S across segment QY. Find the length of segment IL. Express yo... | 11.38 | MATH |
[
{
"content": "Let ZX = 6. Point Q is the reflection of point Z across point X. Line J is the angle bisector of angle ZXQ. Point W is obtained by rotating point Q by angle 5pi/12 about point Z. Point E is the reflection of point Q across point W. Point U is obtained by rotating point Q by angle 7pi/12 about poin... | 1.23 | MATH |
[
{
"content": "VH = 10. Let Y be the midpoint of segment HV. Let G be the rotation of point V by angle pi/3 around point H. Let K be the rotation of point Y by angle 5pi/12 around point V. Let B be the incenter of triangle HKY. Let U be the angle bisector of angle KGV. Point X is the reflection of point K across... | 7.91 | MATH |
[
{
"content": "PO = 3. Point E is obtained by rotating point P by angle pi/6 about point O. Let I be the midpoint of segment EP. Let C be the midpoint of segment IE. Point D is the reflection of point C across point E. What is the inradius of triangle OID? Express your answer as a decimal number rounded to 2 dec... | 0.47 | MATH |
[
{
"content": "Let CV = 12. Let K be the perpendicular bisector of segment CV. Point L is on line K with |LV| = 10. Point J is the reflection of point C across point L. Point F is the reflection of point L across segment VJ. Find the inradius of triangle LFV. Express your answer as a decimal number rounded to 2 ... | 3.4 | MATH |
[
{
"content": "SI = 6. Let W be the rotation of point I by angle pi around point S. Let J be the vector from point W to point I. Let O be the rotation of point W by angle pi/3 around point I. Point B is the translation of point S by vector J. Let E be the perpendicular bisector of segment IO. Let A be the reflec... | 187.06 | MATH |
[
{
"content": "AF = 12. Let T be the reflection of point A across point F. Point Q is obtained by rotating point A by angle 11pi/12 about point F. Let B be the midpoint of segment QF. Point I is the reflection of point B across point T. Let L be the reflection of point I across point A. Let N be the midpoint of ... | 35.18 | MATH |
[
{
"content": "PM = 6. Point V is obtained by rotating point M by angle 2pi/3 about point P. Point W is the reflection of point M across point V. Line J is the perpendicular bisector of segment WV. Point S is the reflection of point P across line J. Point I is the orthocenter of triangle SPV. Find the distance b... | 31.18 | MATH |
[
{
"content": "NY = 10. Let B be the reflection of point Y across point N. Let E be the rotation of point N by angle pi/4 around point Y. Let J be the midpoint of segment EB. Let C be the midpoint of segment NE. Point R is the reflection of point C across segment YN. Let Z be the circumcenter of triangle NRJ. Fi... | 7.94 | MATH |
[
{
"content": "QF = 11. Point Z is the reflection of point F across point Q. Let J be the rotation of point Z by angle 5pi/12 around point F. Point K is the reflection of point J across point Q. Let U be the midpoint of segment ZK. Point E is the reflection of point U across point Z. Find the circumradius of tri... | 17.03 | MATH |
[
{
"content": "YP = 11. Let Q be the reflection of point Y across point P. Let N be the midpoint of segment YP. Let V be the rotation of point N by angle pi/6 around point P. Point J is the reflection of point N across point V. Line W is the angle bisector of angle YQV. Let L be the rotation of point Y by angle ... | 20.77 | MATH |
[
{
"content": "DG = 11. Let L be the line through points G and D. Point K is obtained by rotating point D by angle pi about point G. Let T be the rotation of point G by angle 2pi/3 around point K. Let V be the midpoint of segment GK. Point B is the reflection of point T across line L. Let E be the reflection of ... | 1.03 | MATH |
[
{
"content": "Let VH = 9. Let G be the line through points V and H. Let M be the line through point V perpendicular to line G. Let W be the midpoint of segment VH. Point Z is on line M with |ZW| = 6. Point T is on line G. Line A is the angle bisector of angle TWZ. Line D is the reflection of line A across point... | 3.0 | MATH |
[
{
"content": "IG = 12. Point Y is obtained by rotating point I by angle 5pi/6 about point G. Point Q is the midpoint of segment YG. Point H is the orthocenter of triangle QIG. Point F is the reflection of point H across segment GQ. Find the measure of angle YIF, in radians. Express your answer as a decimal numb... | 250.71 | MATH |
[
{
"content": "Let NF = 9. Let L be the reflection of point N across point F. Let E be the reflection of point F across point L. Point U is obtained by rotating point N by angle 5pi/12 about point F. Let S be the rotation of point U by angle 5pi/12 around point L. Point O is the reflection of point S across segm... | 1.1 | MATH |
[
{
"content": "VC = 7. Point B is obtained by rotating point V by angle pi/4 about point C. Let Z be the rotation of point B by angle pi/3 around point C. Point J is the reflection of point V across point Z. Point F is the reflection of point Z across segment VB. Let T be the midpoint of segment VB. Let Y be the... | 62.21 | MATH |
[
{
"content": "Let TE = 3. Point Q is the midpoint of segment TE. Let G be the rotation of point E by angle pi/2 around point T. Let F be the perpendicular bisector of segment QE. Point P is the reflection of point G across line F. Let R be the orthocenter of triangle GPE. Point Z is the centroid of triangle GPE... | 3.2 | MATH |
[
{
"content": "OC = 5. Let I be the reflection of point O across point C. Let P be the rotation of point O by angle pi/3 around point I. Point W is the reflection of point I across point O. Line E is the perpendicular bisector of segment CP. Let Y be the reflection of point C across point P. Point B is the refle... | 21.65 | MATH |
[
{
"content": "TP = 2. Line W is the perpendicular bisector of segment PT. Let G be the reflection of line W through point P. Point M is on line G with |MP| = 11. Let Z be the midpoint of segment MP. Line K is the perpendicular bisector of segment PZ. Point U is the midpoint of segment ZP. Line O passes through ... | 2.08 | MATH |
[
{
"content": "Line Q is the perpendicular bisector of segment OO. Point L is the reflection of point O across segment R46T. Point V is the reflection of point L across line Q. Let H be the circumcircle of triangle T. Point E is the inversion of point Z with respect to circle H. Point G is the reflection of poin... | 1.32 | MATH |
[
{
"content": "Let HF = 4. Let D be the rotation of point F by angle pi/2 around point H. Let Q be the centroid of triangle HDF. Let U be the incenter of triangle HDF. What is the inradius of triangle QUF? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTex format:... | 0.1 | MATH |
[
{
"content": "QE = 12. Point P is obtained by rotating point E by angle 5pi/6 about point Q. Point S is the reflection of point Q across point E. Let V be the orthocenter of triangle PQE. Point W is the reflection of point E across point S. What is the length of segment WV? Express your answer as a decimal numb... | 60.47 | MATH |
[
{
"content": "Let XA = 2. Point J is the midpoint of segment AX. Let G be the rotation of point A by angle 5pi/12 around point J. Let M be the rotation of point G by angle pi/12 around point A. Let B be the centroid of triangle GJM. Let Q be the midpoint of segment MJ. Point R is the centroid of triangle AQB. L... | 0.3 | MATH |
[
{
"content": "Let VZ = 7. Let W be the rotation of point Z by angle 5pi/6 around point V. Point A is the midpoint of segment ZW. Line Q is the perpendicular bisector of segment VZ. Let U be the line through point W perpendicular to line Q. Point S is the reflection of point V across line U. Find the circumradiu... | 3.73 | MATH |
[
{
"content": "Let TL = 1. Point R is obtained by rotating point L by angle 5pi/12 about point T. Point J is the midpoint of segment LT. Let N be the reflection of point T across point R. Point W is the reflection of point N across point J. Find the distance between points W and N. Express your answer as a decim... | 3.86 | MATH |
[
{
"content": "Let AZ = 2. Let B be the reflection of point Z across point A. Let E be the rotation of point Z by angle 5pi/12 around point A. Point H is the midpoint of segment BE. Point F is the incenter of triangle ZBE. Point X is the reflection of point F across segment ZB. Point W is the reflection of point... | 1.49 | MATH |
[
{
"content": "QC = 5. Point X is obtained by rotating point Q by angle pi/6 about point C. Point Z is the reflection of point C across point Q. Point O is the reflection of point Q across point Z. Let W be the circumcenter of triangle QXC. Let M be the midpoint of segment XC. Point T is the reflection of point ... | 6.25 | MATH |
[
{
"content": "Let EK = 11. Let D be the midpoint of segment EK. Let G be the rotation of point D by angle pi/12 around point E. Line W is the perpendicular bisector of segment GE. Line S is the perpendicular bisector of segment KE. Let P be the line through point E parallel to line S. Let C be the reflection of... | 9.46 | MATH |
[
{
"content": "Let AV = 11. Line P is the perpendicular bisector of segment VA. Point O lies on line P at distance 1 from point A. Let X be the reflection of point A across point O. Let L be the vector from point X to point A. Point Y is the translation of point O by vector L. Line Z passes through points A and ... | 8.22 | MATH |
[
{
"content": "Let QY = 3. Point Z is the midpoint of segment QY. Point B is obtained by rotating point Y by angle pi/4 about point Q. Let K be the centroid of triangle YBQ. Point I is the reflection of point Z across segment YB. Point D is the midpoint of segment KI. What is the measure of angle BDI, in radians... | 0.8 | MATH |
[
{
"content": "HR = 1. Let W be the rotation of point R by angle 5pi/12 around point H. Point Q is obtained by rotating point W by angle pi/3 about point H. Point M is the reflection of point R across point H. Point S is the reflection of point Q across segment RH. Let P be the midpoint of segment WR. Find the i... | 0.3 | MATH |
[
{
"content": "MA = 3. Point P is the midpoint of segment AM. Let N be the rotation of point P by angle 11pi/12 around point M. Line R is the perpendicular bisector of segment NM. Point E is the incenter of triangle MPN. Let B be the line through point P parallel to line R. Point U is the reflection of point A a... | 0.08 | MATH |
[
{
"content": "Let VC = 4. Line G is the perpendicular bisector of segment VC. Line J passes through point V parallel to line G. Point Y is on line J with |YV| = 1. Line H is the reflection of line G across line J. Let L be the midpoint of segment YC. Let A be the midpoint of segment VC. Point I is the reflectio... | 8.02 | MATH |
[
{
"content": "Let XU = 9. Let V be the rotation of point X by angle 2pi/3 around point U. Point A is obtained by rotating point V by angle 11pi/12 about point X. Let Z be the reflection of point U across point V. Let O be the orthocenter of triangle AXZ. Point B is the circumcenter of triangle AXZ. Find the mea... | 752.12 | MATH |
[
{
"content": "DE = 11. Point W is obtained by rotating point E by angle pi/12 about point D. Point M is the reflection of point E across point D. Let S be the rotation of point W by angle 3pi/4 around point M. Point P is the reflection of point S across point D. Point Z is the reflection of point P across segme... | 4.55 | MATH |
[
{
"content": "AT = 11. Point U is the reflection of point T across point A. Point L is obtained by rotating point T by angle 2pi/3 about point A. Point I is the midpoint of segment LT. Point X is the reflection of point I across point U. Point G is the midpoint of segment XT. Point O is the circumcenter of tria... | 38.51 | MATH |
[
{
"content": "GJ = 11. Let H be the rotation of point G by angle 7pi/12 around point J. Point R is the midpoint of segment GH. Let M be the midpoint of segment HR. Point U is obtained by rotating point J by angle pi/12 about point G. Point T is obtained by rotating point U by angle pi/3 about point G. Line N is... | 32.96 | MATH |
[
{
"content": "KG = 2. Let I be the midpoint of segment GK. Point O is obtained by rotating point G by angle 3pi/4 about point I. Y is placed 1 units away from G. Let U be the circumcenter of triangle GIO. Point J is the midpoint of segment IG. Let L be the midpoint of segment IO. Point A is the reflection of po... | 0.57 | MATH |
[
{
"content": "UG = 6. Let H be the rotation of point G by angle 11pi/12 around point U. Point P is the reflection of point H across point G. Point S is the midpoint of segment GU. Let F be the midpoint of segment HG. Point Q is the centroid of triangle GSH. Point O is the reflection of point Q across point P. W... | 34.7 | MATH |
[
{
"content": "XS = 2. Let V be the vector from point X to point S. Point Z is the reflection of point X across point S. Point A is the translation of point Z by vector V. Point Y is obtained by rotating point S by angle 3pi/4 about point A. Let B be the circumcenter of triangle ZXY. Line H is the perpendicular ... | 1.28 | MATH |
[
{
"content": "Let LB = 6. Let W be the rotation of point B by angle 11pi/12 around point L. Point P is the midpoint of segment LW. Point O is the reflection of point P across segment WB. Point T is the reflection of point O across point P. What is the distance between points T and L? Express your answer as a de... | 3.0 | MATH |
[
{
"content": "Let YG = 7. Let B be the rotation of point Y by angle pi/3 around point G. Let K be the midpoint of segment YG. Point R is the reflection of point B across segment GY. Let X be the vector from point R to point K. Point E is the reflection of point G across point B. Point S is the translation of po... | 5.35 | MATH |
[
{
"content": "Let RQ = 1. Point E is obtained by rotating point Q by angle 5pi/12 about point R. Let I be the midpoint of segment RQ. Point O is the centroid of triangle RQE. Circle V is the circumcircle of triangle RQE. Point B is the inversion of point I with respect to circle V. Find the distance between poi... | 0.98 | MATH |
[
{
"content": "Let ZQ = 4. Point E is the reflection of point Q across point Z. Let R be the rotation of point Z by angle 7pi/12 around point E. Let H be the rotation of point E by angle 5pi/12 around point Z. Point N is the reflection of point R across point H. Let K be the midpoint of segment QZ. Let L be the ... | 0.83 | MATH |
[
{
"content": "YB = 9. Let Q be the rotation of point B by angle 5pi/6 around point Y. Let H be the midpoint of segment YQ. Let E be the orthocenter of triangle YBQ. Point T is the midpoint of segment BQ. Point F is the reflection of point T across segment YB. What is the measure of angle HFE, in radians? Expres... | 79.28 | MATH |
[
{
"content": "Let KJ = 4. Point W is obtained by rotating point J by angle 5pi/12 about point K. Line Y is the perpendicular bisector of segment WJ. Let I be the midpoint of segment WK. Point L is the midpoint of segment JW. Point M is the reflection of point I across line Y. Find the distance between points M ... | 2.0 | MATH |
[
{
"content": "JF = 7. Line X is the perpendicular bisector of segment JF. Let O be the reflection of line X through point J. Let Y be the rotation of point J by angle 5pi/6 around point F. Let E be the orthocenter of triangle FJY. Point T is the midpoint of segment JF. Line R is the reflection of line O across ... | 25.32 | MATH |
[
{
"content": "HW = 3. Let E be the rotation of point H by angle 5pi/6 around point W. Let Y be the midpoint of segment WE. Line U is the perpendicular bisector of segment YE. Point P is the reflection of point H across line U. Point F is the circumcenter of triangle PHE. Find the distance between points F and P... | 4.63 | MATH |
[
{
"content": "Let SF = 3. Point K is obtained by rotating point F by angle 5pi/12 about point S. Circle Y is the circumcircle of triangle FSK. Circle H is the reflection of circle Y across point S. Point U is the inversion of point F with respect to circle H. Point J is the orthocenter of triangle FSK. Line A p... | 0.37 | MATH |
[
{
"content": "PJ = 4. Let V be the rotation of point P by angle pi/3 around point J. Point X is the midpoint of segment JV. Circle H is the circumcircle of triangle VXP. Point U is the inversion of point J with respect to circle H. Point D is the centroid of triangle VXP. What is the circumradius of triangle UV... | 1.76 | MATH |
[
{
"content": "IM = 11. Let W be the rotation of point M by angle 11pi/12 around point I. Point D lies on segment IW. Line X is the perpendicular bisector of segment IW. Point V is the reflection of point M across line X. Find the measure of angle VMD, in radians. Express your answer as a decimal number rounded ... | 45.91 | MATH |
[
{
"content": "OJ = 7. Let A be the reflection of point O across point J. Let Y be the perpendicular bisector of segment JA. Point E lies on line Y at distance 3 from point A. Point T is the reflection of point O across line Y. Point G is the circumcenter of triangle TEJ. Point S is the reflection of point G acr... | 12.87 | MATH |
[
{
"content": "YC = 10. Point O is obtained by rotating point C by angle pi/12 about point Y. Let K be the reflection of point C across point Y. Let E be the midpoint of segment KY. Point M is the reflection of point K across segment OY. What is the measure of angle EMO, in radians? Express your answer as a deci... | 31.91 | MATH |
[
{
"content": "FP = 2. Point R is obtained by rotating point P by angle 3pi/4 about point F. Let O be the centroid of triangle FPR. Point S is the midpoint of segment RO. Let C be the orthocenter of triangle FPR. Line J is the angle bisector of angle FOC. Point K is the reflection of point S across line J. What ... | 1.94 | MATH |
[
{
"content": "AO = 8. Point S is obtained by rotating point A by angle 5pi/12 about point O. Line G passes through points A and S. Point J is the reflection of point O across line G. Point Y is the midpoint of segment SO. Let N be the perpendicular bisector of segment SY. Point Q is the reflection of point A ac... | 1.93 | MATH |
[
{
"content": "YH = 2. Point W is the midpoint of segment HY. Let L be the reflection of point W across point H. Point E is obtained by rotating point H by angle 11pi/12 about point L. Let U be the rotation of point L by angle 2pi/3 around point W. Let K be the reflection of point W across point L. Point V is ob... | 3.78 | MATH |
[
{
"content": "Let BX = 11. Let T be the rotation of point B by angle 3pi/4 around point X. Let P be the rotation of point B by angle 5pi/12 around point X. Let Y be the midpoint of segment TX. Circle N is the incircle of triangle PBY. Let W be the orthocenter of triangle PBY. Let E be the inversion of point X i... | 5.25 | MATH |
[
{
"content": "KD = 8. Let P be the rotation of point K by angle 3pi/4 around point D. Line V is the perpendicular bisector of segment KP. Point L is the midpoint of segment PD. Let U be the reflection of line V through point P. Point R is the midpoint of segment PL. Point M is the reflection of point R across l... | 7.07 | MATH |
[
{
"content": "QM = 1. Let C be the rotation of point M by angle pi/12 around point Q. Point A is the reflection of point C across point M. Let O be the angle bisector of angle AQC. Let B be the midpoint of segment CM. Point L is the reflection of point B across line O. Let U be the circumcenter of triangle CBQ.... | 0.41 | MATH |
[
{
"content": "UY = 11. Point Z is the reflection of point Y across point U. Let H be the vector from point Y to point Z. Point M is the midpoint of segment ZU. Let E be the rotation of point Z by angle pi/6 around point U. Let K be point Z translated by vector H. Let G be the rotation of point K by angle pi/12 ... | 7.88 | MATH |
[
{
"content": "FB = 2. Let T be the midpoint of segment BF. Let Z be the reflection of point T across point F. Point O is obtained by rotating point T by angle pi/6 about point Z. Point H is the reflection of point T across segment FO. Line L is the angle bisector of angle TBH. Point C is the reflection of point... | 0.15 | MATH |
[
{
"content": "VQ = 6. Let P be the midpoint of segment QV. Point L is the reflection of point V across point Q. Let C be the perpendicular bisector of segment QV. Line X passes through point V parallel to line C. Line O is the reflection of line X across line C. Point D is the reflection of point P across line ... | 35.49 | MATH |
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