messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
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[
{
"content": "Let CS = 4. Let O be the midpoint of segment SC. Point Z is obtained by rotating point O by angle 5pi/12 about point C. Line H is the angle bisector of angle SCZ. Let F be the reflection of point O across point S. Point X is the midpoint of segment FC. Point B is the reflection of point X across l... | 0.37 | MATH |
[
{
"content": "CY = 12. Point X is the reflection of point C across point Y. Let O be the perpendicular bisector of segment YX. Point G is obtained by rotating point Y by angle pi/2 about point X. Point A is the reflection of point X across point G. Let U be the rotation of point G by angle 7pi/12 around point C... | 26.58 | MATH |
[
{
"content": "GC = 1. Let T be the reflection of point G across point C. Let D be the rotation of point T by angle pi/4 around point G. Line A passes through point T perpendicular to segment DC. Let E be the midpoint of segment DC. Point F is the reflection of point E across line A. Point U is the reflection of... | 2.95 | MATH |
[
{
"content": "Let JN = 3. Let G be the perpendicular bisector of segment JN. Let S be the rotation of point N by angle 5pi/12 around point J. Line C is the reflection of line G across point J. Line E is the perpendicular bisector of segment SJ. Let K be the reflection of line E across line C. Point X is the ref... | 3.79 | MATH |
[
{
"content": "Let HJ = 8. Point U is obtained by rotating point J by angle pi/12 about point H. Let S be the rotation of point H by angle pi/6 around point U. Point F is the midpoint of segment JU. Line X is the perpendicular bisector of segment SU. Point W is the reflection of point F across point S. Point G i... | 8.99 | MATH |
[
{
"content": "VK = 2. Let G be the reflection of point V across point K. Point T is obtained by rotating point V by angle 7pi/12 about point G. Let O be the reflection of point T across point K. Point Q is the reflection of point T across point V. Point I is the reflection of point K across segment OQ. Point W ... | 5.14 | MATH |
[
{
"content": "Let TS = 11. Point B is obtained by rotating point T by angle pi/12 about point S. Point X is the midpoint of segment TB. Let Z be the centroid of triangle TBS. Point O is the reflection of point Z across segment TB. Let H be the reflection of point S across point O. Find the distance between poin... | 18.18 | MATH |
[
{
"content": "AV = 6. Let K be the midpoint of segment AV. Point Q is obtained by rotating point V by angle 5pi/12 about point A. Let P be the angle bisector of angle AVQ. Let Z be the orthocenter of triangle QVK. Point B is the reflection of point Z across line P. Let F be the angle bisector of angle VQA. Let ... | 6.69 | MATH |
[
{
"content": "Let OH = 2. Point C is obtained by rotating point O by angle 11pi/12 about point H. Point Y is the midpoint of segment HC. Line X passes through points O and C. Point I is the reflection of point H across line X. What is the circumradius of triangle IYC? Express your answer as a decimal number rou... | 2.06 | MATH |
[
{
"content": "Let SL = 3. Point R is obtained by rotating point L by angle pi about point S. Line T passes through point L perpendicular to segment LS. Point F is obtained by rotating point R by angle 3pi/4 about point L. Let I be the reflection of line T through point S. Let C be the perpendicular bisector of ... | 10.48 | MATH |
[
{
"content": "FE = 5. Point B is obtained by rotating point F by angle pi/4 about point E. Let I be the orthocenter of triangle BFE. Point V is the centroid of triangle BFE. Point N is the midpoint of segment BI. Find the distance between points V and N. Express your answer as a decimal number rounded to 2 deci... | 1.49 | MATH |
[
{
"content": "AX = 2. Let P be the rotation of point A by angle pi/2 around point X. Point N is obtained by rotating point A by angle pi/12 about point X. Point C is the orthocenter of triangle ANX. Let Z be the midpoint of segment PC. Let Y be the perpendicular bisector of segment AN. Point B is the reflection... | 1.98 | MATH |
[
{
"content": "Let KM = 11. Point C is obtained by rotating point K by angle 7pi/12 about point M. Point X is the circumcenter of triangle KCM. Let Z be the line through point X parallel to segment KC. Segment MK and line Z intersect at point L. Point H is the orthocenter of triangle KCM. Find the length of segm... | 10.84 | MATH |
[
{
"content": "OR = 7. Let A be the midpoint of segment RO. Point I is obtained by rotating point R by angle 7pi/12 about point A. Let N be the angle bisector of angle IOA. Point D is the reflection of point I across line N. Let J be the line through point R perpendicular to line N. Point F is the reflection of ... | 0.33 | MATH |
[
{
"content": "DY = 9. Let N be the rotation of point Y by angle 5pi/6 around point D. Line O passes through point N parallel to segment YD. Point M is the midpoint of segment DY. Let A be the angle bisector of angle NDM. Let U be the perpendicular bisector of segment YD. Let I be the reflection of line O across... | 1.87 | MATH |
[
{
"content": "MK = 8. Point J is the midpoint of segment KM. Point R is obtained by rotating point K by angle pi/4 about point M. Let C be the rotation of point R by angle pi/6 around point J. Let Y be the rotation of point K by angle pi/3 around point R. Line T is the angle bisector of angle YRC. Let L be the ... | 1.05 | MATH |
[
{
"content": "Let PJ = 8. Point C is obtained by rotating point P by angle pi/2 about point J. Circle Y is the circumcircle of triangle CPJ. Let I be the reflection of point P across point J. Let B be the reflection of point C across point J. Let S be the reflection of point J across point I. Let A be the midpo... | 25.51 | MATH |
[
{
"content": "Let UX = 10. Let Y be the midpoint of segment UX. Point Q is the midpoint of segment YU. Let T be the perpendicular bisector of segment XU. Point L is obtained by rotating point Q by angle 11pi/12 about point U. Let V be the reflection of line T through point X. Point R is the reflection of point ... | 0.27 | MATH |
[
{
"content": "Let UK = 3. Let G be the rotation of point K by angle 5pi/6 around point U. Point E is the midpoint of segment GK. Let N be the angle bisector of angle KEG. Point F is the midpoint of segment GU. Point Z is the reflection of point E across point F. Point J is the reflection of point Z across line ... | 1.69 | MATH |
[
{
"content": "TZ = 2. Let Y be the rotation of point T by angle pi/3 around point Z. Point G is the reflection of point Y across point T. Let S be the circumcenter of triangle YZG. Let M be the incircle of triangle YZG. Let V be the inversion of point S in circle M. What is the length of segment VS? Express you... | 0.83 | MATH |
[
{
"content": "Let JD = 7. Let Z be the midpoint of segment DJ. Let I be the rotation of point J by angle pi/6 around point Z. Let O be the midpoint of segment JI. Let R be the circumcenter of triangle ODI. Let N be the midpoint of segment RD. Find the distance between points O and N. Express your answer as a de... | 4.57 | MATH |
[
{
"content": "Let EG = 2. Let R be the rotation of point E by angle 5pi/12 around point G. Let M be the rotation of point E by angle 3pi/4 around point G. Let A be the reflection of point R across point G. Let S be the reflection of point M across point G. Point P is the centroid of triangle SRE. What is the me... | 1.22 | MATH |
[
{
"content": "Let PJ = 5. Point K is the reflection of point P across point J. Let Q be the rotation of point J by angle pi/2 around point P. Point X is the reflection of point K across segment JQ. Let E be the midpoint of segment JQ. Point F is the reflection of point Q across point X. Find the measure of angl... | 56.25 | MATH |
[
{
"content": "PB = 8. Let Z be the rotation of point B by angle 5pi/6 around point P. Let G be the incircle of triangle BPZ. Let Y be the orthocenter of triangle BPZ. Point K is the inversion of point Z with respect to circle G. Let D be the midpoint of segment KY. Find the length of segment PD. Express your an... | 12.85 | MATH |
[
{
"content": "OB = 9. Let C be the rotation of point B by angle 7pi/12 around point O. Let M be the rotation of point C by angle pi/3 around point O. Let A be the rotation of point C by angle pi/12 around point B. Let H be the line through point B perpendicular to segment OB. Let S be the line through point C p... | 12.73 | MATH |
[
{
"content": "Let TU = 5. Let N be the rotation of point U by angle 11pi/12 around point T. Let B be the perpendicular bisector of segment UT. Point M is the reflection of point N across line B. Let X be the reflection of line B through point N. Point H is the reflection of point T across line X. Point Y is the... | 34.17 | MATH |
[
{
"content": "NB = 9. Point K is the midpoint of segment NB. Let J be the midpoint of segment KN. Point M is obtained by rotating point J by angle 5pi/12 about point N. Point V is the reflection of point N across point M. Point L is the circumcenter of triangle VJK. Point R is the reflection of point B across p... | 8.72 | MATH |
[
{
"content": "AU = 5. Point F is the midpoint of segment UA. Point N is obtained by rotating point F by angle pi/2 about point A. Point B is the centroid of triangle AFN. Line O is the perpendicular bisector of segment UA. Point K is the reflection of point B across line O. Point J is the orthocenter of triangl... | 16.01 | MATH |
[
{
"content": "Let DR = 2. Point Z is obtained by rotating point D by angle pi/2 about point R. Let C be the circumcircle of triangle ZDR. Circle P is the reflection of circle C across point Z. Point U is the incenter of triangle ZDR. Let O be the inversion of point U in circle P. What is the measure of angle UO... | 0.94 | MATH |
[
{
"content": "GL = 2. Line N is the perpendicular bisector of segment GL. Point R is on line N with |RL| = 5. Let U be the perpendicular bisector of segment RL. Let X be the incenter of triangle LRG. Let Y be the line through point L parallel to line U. Line A passes through point G parallel to line Y. Point H ... | 2.69 | MATH |
[
{
"content": "Let YK = 10. Let R be the rotation of point K by angle 3pi/4 around point Y. Point S is the midpoint of segment KY. Let Z be the incenter of triangle SKR. Let Q be the centroid of triangle SKR. Find the distance between points Q and Z. Express your answer as a decimal number rounded to 2 decimal p... | 2.97 | MATH |
[
{
"content": "TS = 9. Line K passes through points T and S. Point Q is obtained by rotating point S by angle pi/6 about point T. Let F be the rotation of point S by angle 5pi/12 around point T. Point C is the midpoint of segment TF. Line V passes through point C parallel to line K. Point P is obtained by rotati... | 17.47 | MATH |
[
{
"content": "Let AH = 9. Let X be the midpoint of segment HA. Point G is obtained by rotating point X by angle 7pi/12 about point H. Point C is obtained by rotating point X by angle pi/2 about point H. Let W be the reflection of point C across point G. Point E is the midpoint of segment WA. Point R is the cent... | 1.68 | MATH |
[
{
"content": "RZ = 4. Point D is the midpoint of segment ZR. Let C be the reflection of point D across point Z. Point T is obtained by rotating point C by angle pi/6 about point D. Let Y be the orthocenter of triangle ZCT. Point V is the circumcenter of triangle ZCT. What is the inradius of triangle YVT? Expres... | 0.15 | MATH |
[
{
"content": "TR = 6. Point S is obtained by rotating point R by angle 2pi/3 about point T. Point D is the reflection of point S across point R. Point Z is the midpoint of segment DT. Let U be the centroid of triangle TRS. What is the measure of angle ZTU, in radians? Express your answer as a decimal number rou... | 7.79 | MATH |
[
{
"content": "Point U is the centroid of triangle M. Let W be the line through point U parallel to segment MB. Let E be the reflection of line W through point X. Point R is the reflection of point M across line E. What is the length of segment RB? Express your answer as a decimal number rounded to 2 decimal pla... | 1.53 | MATH |
[
{
"content": "DN = 9. Point U is obtained by rotating point D by angle pi/3 about point N. Let S be the perpendicular bisector of segment UN. Point P is the reflection of point U across point D. Line E is the reflection of line S across point U. Line B is the reflection of line E across point D. Point C is the ... | 23.38 | MATH |
[
{
"content": "ZM = 4. Let X be the rotation of point M by angle pi/12 around point Z. Let C be the centroid of triangle MZX. Point P is the reflection of point C across segment MZ. Let D be the circumcenter of triangle PZC. Find the length of segment DC. Express your answer as a decimal number rounded to 2 deci... | 0.94 | MATH |
[
{
"content": "SK = 12. Point H is obtained by rotating point K by angle 11pi/12 about point S. Point V is the midpoint of segment SK. Point B is the midpoint of segment KH. Point F is the reflection of point S across segment KH. Let Z be the midpoint of segment VS. What is the distance between points Z and F? E... | 4.04 | MATH |
[
{
"content": "HK = 2. Point A is obtained by rotating point H by angle pi/6 about point K. Let V be the circumcircle of triangle AKH. Let R be the incenter of triangle AKH. Let D be the inversion of point R in circle V. Point L is the midpoint of segment AK. Find the distance between points L and D. Express you... | 2.23 | MATH |
[
{
"content": "BI = 10. Point S is obtained by rotating point I by angle 3pi/4 about point B. Let Z be the midpoint of segment SI. Point U is the reflection of point Z across segment BS. Point K is the reflection of point I across segment BS. Find the measure of angle KUZ, in radians. Express your answer as a de... | 1.96 | MATH |
[
{
"content": "UL = 9. Let Z be the rotation of point U by angle pi/2 around point L. Point H is the midpoint of segment UZ. Line K passes through point Z perpendicular to segment LZ. Let B be the rotation of point L by angle 5pi/6 around point U. Line T passes through point U parallel to segment LZ. Point O is ... | 138.31 | MATH |
[
{
"content": "SU = 6. Point F is obtained by rotating point S by angle pi/3 about point U. Let C be the rotation of point F by angle pi/12 around point U. Let G be the angle bisector of angle CFS. Point E is the reflection of point U across line G. Point D is the reflection of point E across segment US. Find th... | 5.2 | MATH |
[
{
"content": "Let IX = 7. Point B is obtained by rotating point I by angle 7pi/12 about point X. Let N be the midpoint of segment XI. Point W is the reflection of point X across segment BI. Let U be the perpendicular bisector of segment BW. Let Z be the angle bisector of angle BNX. Line H is the reflection of l... | 1.13 | MATH |
[
{
"content": "JT = 4. Let L be the midpoint of segment TJ. Line X is the angle bisector of angle JLT. Point Z is the midpoint of segment TL. Point R is on line X with |RL| = 11. Line F passes through points Z and R. Line G is the reflection of line F across point T. Point N is the reflection of point R across l... | 0.32 | MATH |
[
{
"content": "ZO = 12. Point T is the reflection of point Z across point O. Point L is obtained by rotating point T by angle 5pi/6 about point O. Let G be the incircle of triangle TLO. Point U is the orthocenter of triangle TLO. Point V is the inversion of point L with respect to circle G. Find the measure of a... | 238.36 | MATH |
[
{
"content": "GT = 6. Point V is obtained by rotating point T by angle 5pi/12 about point G. Let B be the rotation of point V by angle 5pi/6 around point G. Let H be the midpoint of segment TV. Point Z is the midpoint of segment VB. Let P be the centroid of triangle ZHG. What is the distance between points Z an... | 2.2 | MATH |
[
{
"content": "Let FS = 10. Let E be the vector from point S to point F. Let Q be the midpoint of segment FS. Let U be the rotation of point Q by angle pi/2 around point F. Point A is obtained by rotating point S by angle 11pi/12 about point F. Line X is the angle bisector of angle AQF. Let K be the reflection o... | 124.64 | MATH |
[
{
"content": "Let LN = 10. Point O is the reflection of point N across point L. Let G be the perpendicular bisector of segment NO. Let V be the vector from point O to point N. Point D is the translation of point L by vector V. Point K is on line G with |KL| = 11. Let B be the line through points K and N. Point ... | 2.61 | MATH |
[
{
"content": "BC = 7. Point G is the reflection of point B across point C. Point U is obtained by rotating point C by angle 11pi/12 about point B. Let F be the rotation of point B by angle pi/4 around point C. Let Y be the midpoint of segment FG. Let P be the orthocenter of triangle UBY. Let X be the incenter o... | 412.21 | MATH |
[
{
"content": "Let EA = 3. Let K be the rotation of point A by angle 11pi/12 around point E. Let W be the midpoint of segment AK. Point Z is obtained by rotating point K by angle 11pi/12 about point W. Point T is obtained by rotating point E by angle 5pi/6 about point W. Let S be the rotation of point Z by angle... | 5.03 | MATH |
[
{
"content": "CU = 11. Point D is obtained by rotating point U by angle 5pi/6 about point C. Let H be the centroid of triangle CDU. Point F is the reflection of point C across point D. Let P be the line through points H and F. Line P and segment UC intersect at point V. Point O is the reflection of point V acro... | 25.9 | MATH |
[
{
"content": "KE = 5. Let C be the rotation of point K by angle 5pi/6 around point E. Let M be the centroid of triangle CEK. Point G is the orthocenter of triangle CEK. Let N be the reflection of point M across point C. Let Q be the midpoint of segment MG. What is the measure of angle NKQ, in radians? Express y... | 67.89 | MATH |
[
{
"content": "Let AM = 9. Let Z be the rotation of point M by angle pi/3 around point A. Let F be the circumcenter of triangle MAZ. Point I is the reflection of point F across segment ZM. Point O is the reflection of point I across segment MA. What is the distance between points Z and O? Express your answer as ... | 13.75 | MATH |
[
{
"content": "Let LR = 3. Let Z be the rotation of point R by angle pi/12 around point L. Let Y be the midpoint of segment LR. Point W is the orthocenter of triangle LZY. Let T be the midpoint of segment WR. What is the circumradius of triangle ZTW? Express your answer as a decimal number rounded to 2 decimal p... | 86.39 | MATH |
[
{
"content": "BP = 1. Point S is obtained by rotating point P by angle pi about point B. Let K be the rotation of point S by angle pi/12 around point P. Let G be the midpoint of segment SK. Let X be the circumcenter of triangle BKG. What is the circumradius of triangle KXP? Express your answer as a decimal numb... | 1.9 | MATH |
[
{
"content": "Let GX = 2. Let H be the line through point G perpendicular to segment GX. Let E be the perpendicular bisector of segment GX. Point W is on line E with |WX| = 5. Point C is the midpoint of segment WX. Point L is the reflection of point G across point C. Let Q be the reflection of line E across lin... | 13.75 | MATH |
[
{
"content": "Let LI = 4. Let Q be the rotation of point L by angle 3pi/4 around point I. Line F is the perpendicular bisector of segment IL. Point H is the midpoint of segment IQ. Point D is the reflection of point H across line F. What is the circumradius of triangle DIH? Express your answer as a decimal numb... | 3.96 | MATH |
[
{
"content": "IX = 6. Point D is obtained by rotating point I by angle pi/6 about point X. Let T be the reflection of point I across point D. Point H is the midpoint of segment XT. Let A be the midpoint of segment HT. Find the inradius of triangle AXD. Express your answer as a decimal number rounded to 2 decima... | 0.96 | MATH |
[
{
"content": "Let WD = 8. Point G is the midpoint of segment WD. Point N is obtained by rotating point G by angle pi/2 about point D. Let A be the reflection of point G across point N. Let J be the midpoint of segment WN. Point U is the incenter of triangle AWG. What is the measure of angle UJN, in radians? Exp... | 1.4 | MATH |
[
{
"content": "DU = 4. Point W is obtained by rotating point D by angle 11pi/12 about point U. Let J be the midpoint of segment DW. Let C be the midpoint of segment UW. Let G be the midpoint of segment CJ. What is the inradius of triangle GUW? Express your answer as a decimal number rounded to 2 decimal places.\... | 0.13 | MATH |
[
{
"content": "GT = 1. Let R be the rotation of point T by angle 11pi/12 around point G. Point K is the circumcenter of triangle RGT. Point A is the incenter of triangle RGT. Point S is the midpoint of segment RT. Point J is the midpoint of segment AS. Line F is the perpendicular bisector of segment GT. Point Z ... | 0.98 | MATH |
[
{
"content": "CN = 1. Let F be the rotation of point N by angle 7pi/12 around point C. Point J is the orthocenter of triangle CNF. Let H be the circumcenter of triangle CNF. Let E be the reflection of point N across point C. Let V be the reflection of point J across point N. Find the measure of angle VHE, in ra... | 0.31 | MATH |
[
{
"content": "Let GD = 8. Let Z be the rotation of point D by angle 7pi/12 around point G. Point I is the midpoint of segment DZ. Let N be the line through point I parallel to segment GD. Let W be the centroid of triangle ZGD. Point V is the reflection of point W across line N. What is the distance between poin... | 1.62 | MATH |
[
{
"content": "Line X is the perpendicular bisector of segment O17D. Let Z be the line through point T parallel to line X. Point F is the reflection of point T across segment O17D. Point C is the reflection of point T across line Z. Let M be the circumcenter of triangle D. Find the measure of angle MCF, in radia... | 0.52 | MATH |
[
{
"content": "HS = 2. Let Z be the perpendicular bisector of segment HS. Point K lies on line Z at distance 4 from point S. Point G is the midpoint of segment HK. Point N is the centroid of triangle HKS. Line C is the perpendicular bisector of segment NK. Point F is the reflection of point K across point H. Poi... | 8.13 | MATH |
[
{
"content": "OJ = 9. Let T be the rotation of point O by angle pi/4 around point J. Let H be the reflection of point O across point J. Line F is the angle bisector of angle HOJ. Point Y is the reflection of point T across line F. Find the circumradius of triangle OYT. Express your answer as a decimal number ro... | 9.0 | MATH |
[
{
"content": "Let WZ = 10. Let K be the midpoint of segment ZW. Point O is obtained by rotating point K by angle pi/3 about point Z. Point L is the reflection of point W across point O. Let C be the reflection of point O across point K. Let G be the midpoint of segment LC. Let D be the reflection of point W acr... | 1.24 | MATH |
[
{
"content": "EC = 10. Point A is obtained by rotating point C by angle 7pi/12 about point E. Circle W is the incircle of triangle AEC. Let O be the centroid of triangle AEC. Let M be the inversion of point O in circle W. Find the length of segment MA. Express your answer as a decimal number rounded to 2 decima... | 11.43 | MATH |
[
{
"content": "Let LF = 12. LN = 12. Point S is obtained by rotating point L by angle 2pi/3 about point F. Point Q is the midpoint of segment FL. Let U be the circumcenter of triangle FLN. Point J is the reflection of point S across point U. Point G is the midpoint of segment QJ. What is the length of segment UG... | 7.94 | MATH |
[
{
"content": "HU = 7. Point G is obtained by rotating point H by angle 7pi/12 about point U. Let P be the midpoint of segment HG. Point J is the reflection of point P across segment GU. Point E is the orthocenter of triangle UHG. What is the measure of angle EUJ, in radians? Express your answer as a decimal num... | 1.31 | MATH |
[
{
"content": "AF = 9. Line S passes through points A and F. Point D is obtained by rotating point A by angle 11pi/12 about point F. Point O is the reflection of point D across line S. Let E be the line through point F perpendicular to line S. Point V is on line E. Point I is the reflection of point D across poi... | 15.37 | MATH |
[
{
"content": "Let TB = 9. Point V is obtained by rotating point T by angle pi/12 about point B. Point L is the centroid of triangle BTV. Point Z is the midpoint of segment LB. Point W is the reflection of point L across segment TV. What is the distance between points W and Z? Express your answer as a decimal nu... | 8.92 | MATH |
[
{
"content": "WX = 9. Point P is obtained by rotating point X by angle 5pi/6 about point W. Line L passes through point W perpendicular to segment WX. Let A be the reflection of point X across point P. Line T is the perpendicular bisector of segment WP. Let E be the reflection of line L across line T. Point F i... | 243.94 | MATH |
[
{
"content": "Let GV = 3. Point H is obtained by rotating point V by angle pi/2 about point G. Point Q is the midpoint of segment VH. Let E be the midpoint of segment VG. Point U is the midpoint of segment HE. What is the length of segment QU? Express your answer as a decimal number rounded to 2 decimal places.... | 0.75 | MATH |
[
{
"content": "Let ZK = 11. Point M is the reflection of point Z across point K. Let V be the rotation of point M by angle 5pi/6 around point K. Point O is the reflection of point V across point K. Let I be the midpoint of segment VZ. Point F is the reflection of point I across segment VM. What is the distance b... | 2.85 | MATH |
[
{
"content": "TK = 7. Point C is the reflection of point T across point K. Let G be the rotation of point T by angle pi/3 around point C. Let B be the angle bisector of angle GKT. Point W is the reflection of point G across line B. Let H be the line through points T and K. Line N passes through point G parallel... | 285.68 | MATH |
[
{
"content": "Let OH = 8. Point Z is the reflection of point H across point O. Let I be the midpoint of segment HO. Let M be the reflection of point O across point Z. Let U be the rotation of point I by angle 7pi/12 around point H. Point R is obtained by rotating point U by angle pi/12 about point H. Let W be t... | 3.53 | MATH |
[
{
"content": "VM = 2. Line R passes through points V and M. Let K be the reflection of point M across point V. Point I is obtained by rotating point V by angle pi/6 about point K. Let Z be the midpoint of segment MV. Let G be the reflection of point V across point I. Let O be the reflection of point I across po... | 1.61 | MATH |
[
{
"content": "Let FT = 1. Point G is obtained by rotating point F by angle 3pi/4 about point T. Let L be the midpoint of segment TF. Let U be the incenter of triangle FTG. What is the circumradius of triangle ULG? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in LaTe... | 3.91 | MATH |
[
{
"content": "Let IX = 5. Let N be the rotation of point I by angle pi/3 around point X. Let G be the circumcenter of triangle XIN. Let E be the midpoint of segment XI. Let V be the line through point E perpendicular to segment IN. Point B is the reflection of point I across line V. Point P is the reflection of... | 2.89 | MATH |
[
{
"content": "QP = 4. Let O be the rotation of point P by angle 5pi/6 around point Q. Point V is the centroid of triangle OPQ. Point S is the reflection of point V across point O. Let Z be the reflection of point S across point V. Find the distance between points Z and Q. Express your answer as a decimal number... | 7.73 | MATH |
[
{
"content": "Let WL = 7. Point B is the midpoint of segment WL. Let V be the midpoint of segment WB. Let Q be the angle bisector of angle WVL. Point M is the reflection of point L across point W. Let O be the rotation of point B by angle 7pi/12 around point M. Point P is the reflection of point M across line Q... | 37.99 | MATH |
[
{
"content": "YV = 9. Let K be the vector from point Y to point V. Let X be point V translated by vector K. Let P be the midpoint of segment VX. Let E be the rotation of point P by angle pi/2 around point Y. Let D be the reflection of point V across point E. Let M be the incenter of triangle DPE. Let S be the c... | 1.15 | MATH |
[
{
"content": "Let GF = 11. Let J be the rotation of point F by angle pi/4 around point G. Point B is the reflection of point G across point J. Point C is the orthocenter of triangle GBF. Point H is the midpoint of segment FG. What is the measure of angle CHB, in radians? Express your answer as a decimal number ... | 101.13 | MATH |
[
{
"content": "Let ZG = 1. Let R be the rotation of point Z by angle pi/6 around point G. Let N be the midpoint of segment ZR. Point P is the midpoint of segment NZ. Point J is the reflection of point G across point Z. Let U be the circumcenter of triangle RPG. What is the length of segment JU? Express your answ... | 1.4 | MATH |
[
{
"content": "Let QL = 5. Let K be the rotation of point Q by angle pi/3 around point L. Let Y be the rotation of point K by angle 7pi/12 around point L. Point W is the reflection of point L across segment KY. Let A be the midpoint of segment KW. Let C be the circumcircle of triangle YQL. Point X is the inversi... | 11.27 | MATH |
[
{
"content": "IR = 2. Let Y be the line through points R and I. Let V be the line through point R perpendicular to line Y. Point Z is on line V. Point X is the midpoint of segment IZ. Let H be the midpoint of segment IR. Point N is the centroid of triangle HXZ. What is the distance between points N and X? Expre... | 0.33 | MATH |
[
{
"content": "Let RN = 9. Let H be the rotation of point R by angle pi/2 around point N. Point U is the midpoint of segment HN. Let Y be the orthocenter of triangle RUH. Let M be the circumcircle of triangle RUH. Line B passes through point R perpendicular to segment HR. Point S is the reflection of point N acr... | 54.0 | MATH |
[
{
"content": "DV = 6. Let M be the reflection of point V across point D. Let A be the perpendicular bisector of segment DM. Let H be the vector from point M to point V. Point P is on line A with |PD| = 10. Let W be point P translated by vector H. Point U is the midpoint of segment VP. Let O be the line through ... | 210.0 | MATH |
[
{
"content": "Let MP = 9. Let K be the rotation of point P by angle 3pi/4 around point M. Point N is obtained by rotating point P by angle 2pi/3 about point K. Point Q is obtained by rotating point N by angle 5pi/12 about point P. Let O be the rotation of point M by angle pi/6 around point N. Point Y is the mid... | 12.89 | MATH |
[
{
"content": "Let NQ = 3. Point H is obtained by rotating point N by angle pi/12 about point Q. Point E is the reflection of point Q across segment NH. Point F is the incenter of triangle NHQ. Let P be the reflection of point E across point H. Point W is the reflection of point P across point F. Let Z be the or... | 2.31 | MATH |
[
{
"content": "Let IY = 12. Let O be the rotation of point Y by angle pi/3 around point I. Point B is the midpoint of segment OI. Point J is the centroid of triangle BOY. Point M is the midpoint of segment OY. Find the measure of angle IMJ, in radians. Express your answer as a decimal number rounded to 2 decimal... | 0.52 | MATH |
[
{
"content": "LO = 1. Point F is the reflection of point O across point L. Point P is obtained by rotating point F by angle 2pi/3 about point L. Let W be the rotation of point L by angle pi/2 around point F. Point T is the midpoint of segment FL. Point U is the reflection of point W across point O. Point M is t... | 1.5 | MATH |
[
{
"content": "XQ = 4. Point H is the reflection of point X across point Q. Let Y be the rotation of point H by angle pi/12 around point X. Let M be the midpoint of segment XQ. Point C is the reflection of point H across segment YX. What is the inradius of triangle MYC? Express your answer as a decimal number ro... | 0.87 | MATH |
[
{
"content": "Let IV = 1. Let C be the rotation of point I by angle 5pi/6 around point V. Let H be the orthocenter of triangle IVC. Point B is the reflection of point C across point V. Let R be the midpoint of segment CI. Point Z is the reflection of point B across point R. What is the distance between points Z... | 4.23 | MATH |
[
{
"content": "QF = 7. Let Y be the vector from point Q to point F. Point E is the translation of point F by vector Y. Let M be the rotation of point F by angle 5pi/12 around point Q. Line L is the perpendicular bisector of segment MF. Point U is the reflection of point E across line L. Find the circumradius of ... | 8.78 | MATH |
[
{
"content": "NB = 9. Let J be the rotation of point B by angle pi/12 around point N. Point H is the incenter of triangle NBJ. Point E is on segment BJ. Point I is the midpoint of segment HE. Point W is the midpoint of segment EN. What is the distance between points I and W? Express your answer as a decimal num... | 3.95 | MATH |
[
{
"content": "FQ = 8. Point E is obtained by rotating point F by angle 5pi/6 about point Q. Let H be the reflection of point Q across point F. Point N is the reflection of point H across segment EQ. Let R be the midpoint of segment EN. Let B be the midpoint of segment EQ. Line O passes through point N perpendic... | 33.03 | MATH |
[
{
"content": "QH = 1. Let N be the rotation of point Q by angle pi/2 around point H. Point V is the midpoint of segment HN. Let G be the circumcenter of triangle HVQ. Point F is the incenter of triangle HVQ. Find the measure of angle QFG, in radians. Express your answer as a decimal number rounded to 2 decimal ... | 0.0 | MATH |
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