messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Let AO = 10. Let S be the rotation of point O by angle 3pi/4 around point A. Point M is the midpoint of segment SA. Let V be the circumcenter of triangle SOA. Point P is the reflection of point M across segment OA. What is the measure of angle SVP, in radians? Express your answer as a decimal numb... | 34.34 | MATH |
[
{
"content": "Let LX = 12. Let E be the rotation of point L by angle 11pi/12 around point X. Let A be the rotation of point L by angle 3pi/4 around point E. Point V is the midpoint of segment XL. Point S is the circumcenter of triangle EAX. What is the distance between points S and V? Express your answer as a d... | 20.35 | MATH |
[
{
"content": "NY = 12. Let P be the rotation of point N by angle 11pi/12 around point Y. Point H is the orthocenter of triangle NYP. Let W be the incircle of triangle NYP. Let U be the circumcenter of triangle NYP. Point I is the midpoint of segment PN. Let D be the reflection of circle W through point I. Point... | 46.2 | MATH |
[
{
"content": "Let FM = 10. Let R be the reflection of point F across point M. Point C is obtained by rotating point R by angle 3pi/4 about point F. Point P is obtained by rotating point M by angle 11pi/12 about point R. Point O is the reflection of point F across point C. Line V is the perpendicular bisector of... | 38.69 | MATH |
[
{
"content": "Let XQ = 2. Let J be the rotation of point Q by angle 3pi/4 around point X. Point F is the incenter of triangle QJX. Point Y is the reflection of point F across point Q. Point K is the centroid of triangle QJX. Let W be the midpoint of segment QJ. What is the circumradius of triangle KYW? Express ... | 1.88 | MATH |
[
{
"content": "Let VE = 11. Point G is obtained by rotating point V by angle pi/12 about point E. Let U be the circumcenter of triangle EGV. Point N is the reflection of point U across segment EG. What is the inradius of triangle GNU? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresen... | 0.74 | MATH |
[
{
"content": "NR = 11. Line Z is the perpendicular bisector of segment NR. Point M is the reflection of point N across point R. Point B is on line Z with |BR| = 5. Point W is the reflection of point M across point N. Line E is the angle bisector of angle MNB. Line Y passes through point M perpendicular to line ... | 27.49 | MATH |
[
{
"content": "Let IL = 3. Point N is obtained by rotating point I by angle 7pi/12 about point L. Point A is the midpoint of segment NI. Let Z be the midpoint of segment AL. Let F be the midpoint of segment NA. Find the length of segment ZF. Express your answer as a decimal number rounded to 2 decimal places.\n\... | 1.5 | MATH |
[
{
"content": "NR = 8. Let W be the reflection of point N across point R. Let C be the rotation of point R by angle 7pi/12 around point W. Let F be the vector from point N to point R. Let P be the midpoint of segment RN. Point S is the translation of point P by vector F. Let V be the angle bisector of angle NCP.... | 1.44 | MATH |
[
{
"content": "ZQ = 9. Point V is the midpoint of segment QZ. Line S passes through points Q and V. Line W passes through point V perpendicular to line S. Point A lies on line W at distance 7 from point Q. Let D be the midpoint of segment VA. Point P is the reflection of point Q across point A. Point I is the re... | 12.29 | MATH |
[
{
"content": "OK = 7. Let Q be the rotation of point K by angle 7pi/12 around point O. Let T be the reflection of point Q across point O. Point U is the reflection of point K across point T. Point H is obtained by rotating point K by angle pi/3 about point O. Let W be the incircle of triangle KTH. Circle M is t... | 17.45 | MATH |
[
{
"content": "ED = 8. Point X is obtained by rotating point D by angle pi/6 about point E. Line G passes through points X and D. Point S is the reflection of point E across line G. Let L be the orthocenter of triangle EXS. Let I be the midpoint of segment SL. Find the length of segment SI. Express your answer a... | 14.93 | MATH |
[
{
"content": "ZE = 5. Point Y is obtained by rotating point Z by angle 2pi/3 about point E. Point P is obtained by rotating point E by angle pi/12 about point Z. Let H be the rotation of point Y by angle pi/3 around point Z. Let F be the incenter of triangle HZP. Let A be the incircle of triangle HZP. Point W i... | 0.08 | MATH |
[
{
"content": "Let PJ = 7. Let L be the rotation of point J by angle pi/6 around point P. Point A is the midpoint of segment JP. Point V is the incenter of triangle JPL. Point D is the orthocenter of triangle JPL. Line T is the perpendicular bisector of segment VD. Point N is the reflection of point A across lin... | 4.89 | MATH |
[
{
"content": "TL = 6. Let D be the reflection of point T across point L. Let H be the rotation of point T by angle 2pi/3 around point D. Let S be the rotation of point T by angle pi/12 around point L. Point B is the reflection of point S across point H. Let X be the midpoint of segment BL. Point I is the reflec... | 166.9 | MATH |
[
{
"content": "KE = 7. Let T be the rotation of point E by angle pi/4 around point K. Let D be the midpoint of segment TK. Point P is the midpoint of segment ET. Let A be the perpendicular bisector of segment ED. Let S be the line through point E perpendicular to line A. Point X is the reflection of point P acro... | 6.14 | MATH |
[
{
"content": "Let RC = 7. Let S be the line through points R and C. Let U be the midpoint of segment CR. Point X is obtained by rotating point C by angle 5pi/6 about point R. Let A be the midpoint of segment XR. Point Z is the reflection of point X across line S. Let L be the midpoint of segment ZU. Let P be th... | 3.06 | MATH |
[
{
"content": "Let ZX = 12. Line C is the perpendicular bisector of segment XZ. Let T be the reflection of point X across point Z. Line E passes through point X parallel to line C. Let B be the rotation of point T by angle pi/3 around point Z. Let J be the midpoint of segment TZ. Let Y be the reflection of line ... | 31.75 | MATH |
[
{
"content": "LK = 1. Point A is obtained by rotating point L by angle 7pi/12 about point K. Let T be the midpoint of segment AL. Let S be the centroid of triangle LAK. Let W be the incircle of triangle LAK. Point D is the inversion of point S with respect to circle W. What is the distance between points T and ... | 0.82 | MATH |
[
{
"content": "KA = 10. Point E is obtained by rotating point A by angle 2pi/3 about point K. Let O be the midpoint of segment EA. Point L is obtained by rotating point A by angle pi/6 about point O. Point D is the reflection of point E across segment AK. Point H is the midpoint of segment OD. Point V is the ref... | 15.73 | MATH |
[
{
"content": "XE = 6. Point Q is obtained by rotating point X by angle 5pi/6 about point E. Point I is the incenter of triangle EQX. Point F is the midpoint of segment EQ. Let J be the perpendicular bisector of segment XE. Let M be the midpoint of segment QX. Let C be the midpoint of segment IM. Point A is the ... | 8.3 | MATH |
[
{
"content": "Let AM = 4. Point H is the midpoint of segment AM. Let K be the reflection of point A across point M. Let B be the perpendicular bisector of segment KA. Point C lies on line B at distance 1 from point A. Let R be the reflection of line B through point A. Point X lies on line R. Let Q be the circum... | 1.0 | MATH |
[
{
"content": "Let PN = 1. Let O be the reflection of point P across point N. Point X is obtained by rotating point N by angle 7pi/12 about point P. Point I is the midpoint of segment XP. Let Z be the circumcenter of triangle OIX. Point C is the midpoint of segment ZI. What is the length of segment CZ? Express y... | 0.33 | MATH |
[
{
"content": "GP = 3. Let C be the midpoint of segment PG. Let W be the line through point P perpendicular to segment GC. Point E is obtained by rotating point P by angle pi/12 about point G. Point V is the reflection of point E across line W. Let R be the line through points E and C. Let J be the rotation of p... | 0.48 | MATH |
[
{
"content": "VE = 4. Let N be the rotation of point V by angle pi/12 around point E. Point W is the midpoint of segment EN. Let J be the midpoint of segment WE. Let Y be the angle bisector of angle JVN. Let L be the line through point W perpendicular to line Y. Let X be the line through point W perpendicular t... | 1.66 | MATH |
[
{
"content": "ZH = 3. Let U be the rotation of point Z by angle 7pi/12 around point H. Let R be the incenter of triangle UHZ. Let Q be the midpoint of segment HR. Point A is the midpoint of segment ZQ. Let Y be the line through point R parallel to segment HZ. Point N is the intersection of segment UH and line Y... | 1.97 | MATH |
[
{
"content": "AP = 2. Let Q be the rotation of point P by angle 5pi/6 around point A. Let D be the rotation of point Q by angle 11pi/12 around point A. Point R is the reflection of point Q across point D. Let W be the incenter of triangle QAP. Let S be the orthocenter of triangle QAP. Line K passes through poin... | 6.46 | MATH |
[
{
"content": "Let ZV = 8. Line D passes through points V and Z. Point L is the midpoint of segment ZV. Point A lies on line D at distance 12 from point V. Point J is obtained by rotating point Z by angle 2pi/3 about point V. Point X is the midpoint of segment AJ. Let P be the midpoint of segment JX. Point I is ... | 7.79 | MATH |
[
{
"content": "Let MQ = 6. Let K be the rotation of point M by angle pi/4 around point Q. Let W be the vector from point K to point M. Let E be the reflection of point Q across point K. Point L is the orthocenter of triangle QKM. Point I is the circumcenter of triangle QKM. Let C be the midpoint of segment QK. L... | 8.24 | MATH |
[
{
"content": "Let NY = 7. Let E be the midpoint of segment NY. Let L be the midpoint of segment EY. Line S is the perpendicular bisector of segment NE. Point G is on line S with |GE| = 7. Let W be the reflection of point L across point N. Point O is the midpoint of segment EG. Let C be the midpoint of segment G... | 3.48 | MATH |
[
{
"content": "JP = 11. Let L be the line through points J and P. Point W is obtained by rotating point J by angle 5pi/12 about point P. Point E is obtained by rotating point J by angle pi/12 about point W. Point R is the reflection of point W across line L. Point Y is the reflection of point P across segment EW... | 3.34 | MATH |
[
{
"content": "Let WT = 5. Point A is obtained by rotating point W by angle 7pi/12 about point T. Point I is the reflection of point A across segment TW. Line V passes through points I and T. Point N is the intersection of segment WA and line V. What is the distance between points N and W? Express your answer as... | 5.23 | MATH |
[
{
"content": "VU = 7. Let J be the vector from point V to point U. Let S be point U translated by vector J. Let W be the rotation of point U by angle 7pi/12 around point S. Point T is the reflection of point W across point V. Let O be the midpoint of segment UV. Circle Y is the circumcircle of triangle OTW. Let... | 388.31 | MATH |
[
{
"content": "LV = 9. Point T is obtained by rotating point L by angle 3pi/4 about point V. Line W is the perpendicular bisector of segment TL. Point F is the midpoint of segment VL. Point S is the reflection of point F across line W. Point X is the reflection of point F across point T. Let I be the reflection ... | 28.64 | MATH |
[
{
"content": "Let AO = 6. Let W be the perpendicular bisector of segment OA. Let L be the rotation of point A by angle pi around point O. Let I be the midpoint of segment AO. Let U be the perpendicular bisector of segment LI. Point B is obtained by rotating point I by angle pi/4 about point A. Line Q is the ref... | 6.95 | MATH |
[
{
"content": "NQ = 1. Let T be the rotation of point N by angle pi/6 around point Q. Line S is the perpendicular bisector of segment QT. Line Z is the reflection of line S across point Q. Point Y is the reflection of point T across line Z. What is the inradius of triangle NYT? Express your answer as a decimal n... | 0.23 | MATH |
[
{
"content": "BL = 4. Let Y be the rotation of point L by angle pi/12 around point B. Let I be the orthocenter of triangle BYL. Let X be the midpoint of segment LB. Let K be the reflection of point Y across point B. What is the measure of angle IKX, in radians? Express your answer as a decimal number rounded to... | 0.53 | MATH |
[
{
"content": "Let BF = 7. Let V be the reflection of point F across point B. Point D is obtained by rotating point V by angle 7pi/12 about point F. Point L is the reflection of point B across point D. Point I is the midpoint of segment BV. Let G be the reflection of point L across point I. What is the circumrad... | 374.18 | MATH |
[
{
"content": "Let RU = 7. Let Y be the rotation of point U by angle pi/3 around point R. Point M is obtained by rotating point Y by angle 5pi/6 about point R. Point K is the reflection of point R across point U. Let H be the circumcircle of triangle MRY. Let N be the inversion of point K in circle H. What is th... | 23.42 | MATH |
[
{
"content": "JT = 9. Point R is the reflection of point T across point J. Line Y is the angle bisector of angle RTJ. Let E be the rotation of point J by angle 3pi/4 around point R. Point X is the midpoint of segment ER. Line C is the perpendicular bisector of segment XR. Point F lies on line Y. Point D is the ... | 3.32 | MATH |
[
{
"content": "Let QO = 3. Point Y is obtained by rotating point O by angle pi/12 about point Q. Let V be the midpoint of segment QO. Let H be the midpoint of segment YO. Let G be the rotation of point Y by angle pi/4 around point V. Line W is the angle bisector of angle GQY. Point J is the reflection of point H... | 0.07 | MATH |
[
{
"content": "Let YT = 4. Let D be the rotation of point Y by angle 7pi/12 around point T. Point X is obtained by rotating point T by angle pi/12 about point D. Let F be the incenter of triangle DXY. Line B is the perpendicular bisector of segment XY. Line V passes through point F parallel to line B. Point L is... | 1.51 | MATH |
[
{
"content": "Let YM = 5. Point Z is obtained by rotating point Y by angle 11pi/12 about point M. Point G is obtained by rotating point M by angle pi/12 about point Y. Let Q be the reflection of point Y across point Z. Let R be the reflection of point Z across point Q. Let K be the midpoint of segment ZG. Find ... | 33.1 | MATH |
[
{
"content": "Let MN = 12. Let Z be the rotation of point M by angle 5pi/6 around point N. Let O be the midpoint of segment ZM. Let L be the circumcenter of triangle ONZ. Let V be the incenter of triangle ONZ. What is the distance between points L and V? Express your answer as a decimal number rounded to 2 deci... | 2.53 | MATH |
[
{
"content": "Let ON = 7. Point W is the reflection of point N across point O. Let K be the rotation of point O by angle pi/12 around point N. Line U is the perpendicular bisector of segment NW. Point M is the reflection of point N across segment WK. Point A is the reflection of point M across line U. Find the ... | 10.7 | MATH |
[
{
"content": "QU = 12. Let E be the reflection of point Q across point U. Point J is obtained by rotating point E by angle 3pi/4 about point U. Let Z be the reflection of point Q across point J. Point N is the midpoint of segment ZJ. Point X is the reflection of point U across segment EZ. Find the inradius of t... | 4.21 | MATH |
[
{
"content": "WF = 2. Let D be the reflection of point W across point F. Let O be the rotation of point F by angle pi/2 around point D. Point H is obtained by rotating point D by angle pi/4 about point F. Let A be the centroid of triangle OWF. Point U is the reflection of point O across segment WF. Let G be the... | 0.47 | MATH |
[
{
"content": "LP = 9. Point R is obtained by rotating point L by angle pi/4 about point P. Line X is the perpendicular bisector of segment RP. Let W be the midpoint of segment PL. Line N is the reflection of line X across point L. Let F be the midpoint of segment WR. Let O be the angle bisector of angle FLW. Le... | 6.82 | MATH |
[
{
"content": "XE = 9. Point S is obtained by rotating point E by angle 5pi/6 about point X. Let C be the reflection of point X across point S. Let N be the vector from point S to point X. Let H be point E translated by vector N. Line W is the angle bisector of angle HSC. Point I is the midpoint of segment HX. P... | 10.05 | MATH |
[
{
"content": "Let SE = 5. Let W be the rotation of point E by angle pi/12 around point S. Let V be the rotation of point W by angle pi/12 around point S. Point T is obtained by rotating point W by angle pi/3 about point S. Let P be the reflection of point T across point E. Let J be the midpoint of segment VW. F... | 0.41 | MATH |
[
{
"content": "OY = 9. Point W is obtained by rotating point O by angle pi/2 about point Y. Let P be the rotation of point Y by angle 7pi/12 around point O. Point V is the reflection of point O across point Y. Let U be the angle bisector of angle OPY. Point D is the reflection of point W across line U. What is t... | 0.08 | MATH |
[
{
"content": "Let IF = 8. Point B is obtained by rotating point I by angle 5pi/12 about point F. Point D is the incenter of triangle IBF. Point Z is the midpoint of segment DB. Let R be the circumcenter of triangle IBF. Find the length of segment ZR. Express your answer as a decimal number rounded to 2 decimal ... | 2.6 | MATH |
[
{
"content": "Let YA = 7. Point K is obtained by rotating point Y by angle pi/6 about point A. Point T is the reflection of point K across segment AY. Let V be the centroid of triangle KTA. What is the distance between points Y and V? Express your answer as a decimal number rounded to 2 decimal places.\n\nPrese... | 2.96 | MATH |
[
{
"content": "WP = 2. Line T is the perpendicular bisector of segment WP. Point A lies on line T at distance 10 from point W. Point U is the midpoint of segment PW. Let M be the midpoint of segment UA. Point L is the orthocenter of triangle WAP. What is the distance between points M and L? Express your answer a... | 4.9 | MATH |
[
{
"content": "VY = 12. Point C is the midpoint of segment YV. Point E is obtained by rotating point V by angle pi/2 about point C. Point Q is obtained by rotating point Y by angle pi/12 about point C. Let D be the incircle of triangle QVE. Let G be the reflection of circle D through point Y. Point B is the inve... | 11.34 | MATH |
[
{
"content": "CP = 6. Point A is obtained by rotating point C by angle 11pi/12 about point P. Let F be the perpendicular bisector of segment AC. Let L be the reflection of point A across point C. Point M is the reflection of point L across line F. What is the distance between points M and L? Express your answer... | 35.69 | MATH |
[
{
"content": "KU = 5. Point A is obtained by rotating point U by angle 5pi/12 about point K. Point S is the reflection of point K across point U. Let T be the perpendicular bisector of segment AS. Let L be the circumcenter of triangle KAU. Let H be the line through point L parallel to line T. Point E is the ref... | 3.32 | MATH |
[
{
"content": "Let CJ = 2. Point H is obtained by rotating point C by angle pi/3 about point J. Point D is the reflection of point C across point J. Point W is the reflection of point H across segment CJ. Let S be the circumcenter of triangle HCJ. What is the measure of angle DWS, in radians? Express your answer... | 1.05 | MATH |
[
{
"content": "QA = 10. Let V be the reflection of point Q across point A. Point P is obtained by rotating point V by angle pi/2 about point Q. Let F be the midpoint of segment QP. Point E is the reflection of point A across point Q. Line T passes through point E parallel to segment QP. Point C is the reflection... | 5.1 | MATH |
[
{
"content": "Let PZ = 1. Point G is the midpoint of segment ZP. Point Y is obtained by rotating point Z by angle 3pi/4 about point G. Let S be the midpoint of segment YZ. Let Q be the midpoint of segment GZ. Let H be the angle bisector of angle SGY. Let V be the midpoint of segment YG. Point A is the reflectio... | 0.14 | MATH |
[
{
"content": "Let GA = 11. Let S be the vector from point G to point A. Let P be the rotation of point A by angle 11pi/12 around point G. Let Q be the midpoint of segment GP. Point T is the translation of point P by vector S. Circle B is the circumcircle of triangle TQA. Point H is the incenter of triangle TQA.... | 16.59 | MATH |
[
{
"content": "Let MU = 2. Let K be the rotation of point M by angle pi/3 around point U. Let P be the rotation of point K by angle 5pi/6 around point M. Let C be the perpendicular bisector of segment PK. Point F is the reflection of point U across line C. Let S be the midpoint of segment UM. Let H be the reflec... | 0.14 | MATH |
[
{
"content": "PU = 7. Point H is obtained by rotating point P by angle 2pi/3 about point U. Let I be the midpoint of segment PU. Point Q is the midpoint of segment HP. Let W be the midpoint of segment HU. What is the circumradius of triangle IWQ? Express your answer as a decimal number rounded to 2 decimal plac... | 3.5 | MATH |
[
{
"content": "Let JI = 2. Point T is obtained by rotating point J by angle 2pi/3 about point I. Let L be the midpoint of segment TJ. Circle R is the circumcircle of triangle JIT. Point K is the inversion of point L with respect to circle R. Point U is the incenter of triangle JIT. Let Q be the midpoint of segme... | 0.52 | MATH |
[
{
"content": "Let HZ = 5. Line Y is the perpendicular bisector of segment HZ. Point C is the reflection of point H across point Z. Point K is on line Y with |KZ| = 5. Let Q be the reflection of point H across point C. Point J is the reflection of point Q across segment KH. Point N is the reflection of point Q a... | 132.5 | MATH |
[
{
"content": "Let KU = 10. Let J be the vector from point K to point U. Point M is obtained by rotating point K by angle pi/3 about point U. Point P is the translation of point U by vector J. Let I be the midpoint of segment UP. Point D is the reflection of point I across point P. Let V be the incenter of trian... | 113.28 | MATH |
[
{
"content": "EG = 3. Let L be the perpendicular bisector of segment GE. Point D is on line L with |DG| = 1. Line A is the angle bisector of angle EGD. Line U is the reflection of line L across line A. Line Z is the reflection of line A across point D. Point M is the reflection of point G across line Z. Segment... | 0.96 | MATH |
[
{
"content": "Let VT = 7. Point J is obtained by rotating point V by angle 2pi/3 about point T. Let C be the incenter of triangle TVJ. Let I be the reflection of point T across point V. Let Z be the midpoint of segment IC. Find the distance between points Z and V. Express your answer as a decimal number rounded... | 0.94 | MATH |
[
{
"content": "PS = 4. Let J be the rotation of point S by angle pi/12 around point P. Let V be the midpoint of segment PJ. Let O be the midpoint of segment VJ. Line T is the perpendicular bisector of segment OS. Point A is the reflection of point V across line T. Point E is the midpoint of segment JA. Point Q i... | 2.19 | MATH |
[
{
"content": "NI = 3. Let V be the rotation of point N by angle 7pi/12 around point I. Point W is obtained by rotating point I by angle 2pi/3 about point N. Point F is the midpoint of segment WV. Point R is the reflection of point V across segment NI. Let Z be the line through points F and R. Line Z and segment... | 4.61 | MATH |
[
{
"content": "DN = 8. Let I be the midpoint of segment DN. Let P be the rotation of point D by angle pi/2 around point N. Point E is the reflection of point P across point N. Point M is obtained by rotating point P by angle 11pi/12 about point N. Point L is the midpoint of segment IM. Point X is the midpoint of... | 6.62 | MATH |
[
{
"content": "Let LB = 8. Point J is obtained by rotating point L by angle 3pi/4 about point B. Let C be the circumcenter of triangle LJB. Point A is the reflection of point J across point L. Let M be the midpoint of segment BL. Find the measure of angle MCA, in radians. Express your answer as a decimal number ... | 7.54 | MATH |
[
{
"content": "AY = 5. Let R be the rotation of point A by angle 11pi/12 around point Y. Point L is the reflection of point R across point A. Let M be the reflection of point Y across point L. Point V is the midpoint of segment AM. Let J be the centroid of triangle RAV. Let X be the incenter of triangle RAV. Wha... | 0.21 | MATH |
[
{
"content": "Let TH = 8. Let Z be the rotation of point H by angle pi/12 around point T. Point F is the reflection of point T across point H. Circle R is the incircle of triangle FZT. Point I is the reflection of point H across segment ZT. Point A is the circumcenter of triangle FZT. Let N be the reflection of... | 0.11 | MATH |
[
{
"content": "Let UG = 12. Point Z is the reflection of point U across point G. UR = 12. Point B is the reflection of point R across point Z. Let W be the circumcenter of triangle UZB. Point S is the reflection of point W across segment UZ. What is the distance between points S and Z? Express your answer as a d... | 4.0 | MATH |
[
{
"content": "US = 4. Point D is obtained by rotating point U by angle pi/3 about point S. Let H be the orthocenter of triangle DUS. Point I is the reflection of point D across segment US. Point L is the reflection of point I across segment DU. Find the length of segment LH. Express your answer as a decimal num... | 6.11 | MATH |
[
{
"content": "HS = 2. Point M is obtained by rotating point S by angle 5pi/12 about point H. Let G be the line through point M parallel to segment SH. Point O is the reflection of point H across line G. Point D is the reflection of point M across segment SH. What is the circumradius of triangle DOS? Express you... | 3.21 | MATH |
[
{
"content": "Let BN = 3. Point H is the reflection of point B across point N. Let T be the reflection of point H across point B. Line J is the angle bisector of angle HBT. Point M lies on line J at distance 5 from point N. Point Y is the reflection of point B across point H. Point P is obtained by rotating poi... | 6.23 | MATH |
[
{
"content": "Let XY = 2. Line Q is the perpendicular bisector of segment XY. Point F is on line Q with |FX| = 11. Let G be the reflection of point F across point X. Let D be the line through point Y perpendicular to segment XY. Let H be the line through point G perpendicular to segment XY. Point W is the refle... | 6.26 | MATH |
[
{
"content": "Let SR = 7. Point K is obtained by rotating point R by angle 5pi/6 about point S. Let L be the midpoint of segment KR. Point M is the midpoint of segment SK. Point U is the reflection of point L across point M. Find the circumradius of triangle UKR. Express your answer as a decimal number rounded ... | 6.82 | MATH |
[
{
"content": "Let MC = 12. Point T is the reflection of point C across point M. Let I be the rotation of point M by angle 3pi/4 around point C. Let F be the perpendicular bisector of segment MI. Let A be the centroid of triangle TMI. Point P is the midpoint of segment AC. Point J is the reflection of point P ac... | 26.58 | MATH |
[
{
"content": "BR = 6. Let X be the rotation of point R by angle pi around point B. Point S is the reflection of point R across point X. Point J is the reflection of point X across point R. Point V is obtained by rotating point B by angle 3pi/4 about point J. Let D be the line through points B and V. Point G is ... | 1.51 | MATH |
[
{
"content": "ZJ = 5. Point G is the reflection of point Z across point J. Line Y is the perpendicular bisector of segment ZG. Point T is the midpoint of segment GJ. Point X is on line Y with |XT| = 5. Let Q be the line through point Z parallel to line Y. Point O is the reflection of point T across line Q. Let ... | 31.25 | MATH |
[
{
"content": "RJ = 1. Point K is obtained by rotating point J by angle pi/4 about point R. Line C is the perpendicular bisector of segment JR. Let M be the rotation of point J by angle 3pi/4 around point R. Let T be the midpoint of segment KM. Point O is the reflection of point T across line C. Point A is the m... | 2.09 | MATH |
[
{
"content": "Let TE = 10. Point P is the midpoint of segment TE. Let I be the rotation of point E by angle 7pi/12 around point T. Let L be the midpoint of segment IP. Let N be the midpoint of segment EI. Point B is the reflection of point N across segment PE. Let R be the midpoint of segment BI. What is the di... | 2.5 | MATH |
[
{
"content": "IL = 5. Let A be the midpoint of segment IL. Line M is the perpendicular bisector of segment IL. Let F be the line through point L parallel to line M. Point S is the midpoint of segment IA. Let K be the rotation of point I by angle 5pi/12 around point S. Let W be the reflection of point L across p... | 6.56 | MATH |
[
{
"content": "CJ = 11. Point I is obtained by rotating point C by angle 3pi/4 about point J. Let V be the rotation of point C by angle 11pi/12 around point J. Point L is the reflection of point C across point V. Let K be the circumcenter of triangle IVL. Point H is the orthocenter of triangle IVL. What is the m... | 96.89 | MATH |
[
{
"content": "CG = 7. Point X is obtained by rotating point C by angle pi/6 about point G. Point E is the reflection of point G across point C. Let R be the rotation of point G by angle pi/2 around point X. Let U be the angle bisector of angle GXR. Point B is the reflection of point C across line U. Point T is ... | 6.79 | MATH |
[
{
"content": "EN = 11. Point F is the reflection of point N across point E. Let T be the reflection of point F across point N. Line L is the perpendicular bisector of segment ET. Point O lies on line L at distance 4 from point N. Point G lies on line L at distance 6 from point F. Point P is the reflection of po... | 38.96 | MATH |
[
{
"content": "EM = 2. Point D is obtained by rotating point M by angle pi/6 about point E. Let A be the midpoint of segment ME. Point Z is the centroid of triangle DAE. Point U is the incenter of triangle DAE. What is the length of segment ZU? Express your answer as a decimal number rounded to 2 decimal places.... | 0.1 | MATH |
[
{
"content": "AO = 4. Let E be the rotation of point O by angle pi/3 around point A. Point X is obtained by rotating point E by angle pi/4 about point O. Let Z be the midpoint of segment OX. Point Y is the reflection of point X across segment AZ. Point I is the incenter of triangle EAZ. What is the circumradius... | 1.75 | MATH |
[
{
"content": "Let WG = 3. Let Q be the vector from point G to point W. Point Y is the translation of point W by vector Q. Line M is the perpendicular bisector of segment WG. Point O is the midpoint of segment YW. Let J be the rotation of point G by angle 2pi/3 around point O. Let L be the line through point O p... | 0.46 | MATH |
[
{
"content": "Let SN = 2. Let P be the perpendicular bisector of segment SN. Point Y is obtained by rotating point S by angle pi/2 about point N. Point K is obtained by rotating point N by angle 5pi/6 about point Y. Point G is the reflection of point Y across line P. Point Q is the reflection of point K across ... | 2.0 | MATH |
[
{
"content": "Let HS = 2. Point T is obtained by rotating point H by angle pi/6 about point S. Line W passes through points S and T. Point C is the reflection of point H across line W. Point E is the reflection of point C across point T. Point R is the midpoint of segment HE. What is the circumradius of triangl... | 2.24 | MATH |
[
{
"content": "Let FI = 12. Let R be the rotation of point I by angle 2pi/3 around point F. Let P be the circumcenter of triangle RIF. Let H be the incenter of triangle RIF. Point G is the midpoint of segment IH. Let T be the midpoint of segment PF. Point Q is the midpoint of segment TP. Find the length of segme... | 5.44 | MATH |
[
{
"content": "Let NG = 2. Let V be the rotation of point G by angle 5pi/6 around point N. Point Z is the reflection of point G across point N. Let H be the line through point N perpendicular to segment GN. Point T is the midpoint of segment VZ. Point Q is the reflection of point T across line H. Point E is the ... | 0.07 | MATH |
[
{
"content": "WY = 9. Point A is the midpoint of segment YW. Point T is obtained by rotating point W by angle pi/12 about point A. Point N is the reflection of point Y across segment TA. Let I be the midpoint of segment NT. What is the distance between points T and I? Express your answer as a decimal number rou... | 4.46 | MATH |
[
{
"content": "Let CS = 8. Let I be the rotation of point S by angle pi/6 around point C. Point K is the reflection of point I across point C. Let D be the angle bisector of angle CSK. Point G is the reflection of point K across line D. Let X be the reflection of line D through point K. Point V is the midpoint o... | 5.9 | MATH |
[
{
"content": "RM = 2. Point C is obtained by rotating point R by angle pi/6 about point M. Line H is the perpendicular bisector of segment MR. Let T be the midpoint of segment RC. Let I be the line through point T parallel to line H. Point K is the reflection of point C across segment MR. Point L is the reflect... | 0.37 | MATH |
[
{
"content": "Let DQ = 6. Line A is the perpendicular bisector of segment DQ. Let O be the rotation of point Q by angle 7pi/12 around point D. Let F be the reflection of point Q across point O. Let I be the reflection of point D across point Q. Point G is the reflection of point I across line A. What is the inr... | 3.23 | MATH |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.