messages listlengths 1 1 | ground_truth stringlengths 3 7 | dataset stringclasses 1 value |
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[
{
"content": "Let ZP = 9. Let B be the rotation of point Z by angle 5pi/6 around point P. Point W is the orthocenter of triangle BPZ. Point S is the centroid of triangle BPZ. Point Y is the incenter of triangle BPZ. Point U is the reflection of point S across segment ZB. Point J is the midpoint of segment YU. F... | 0.26 | MATH |
[
{
"content": "Let WM = 7. Point K is obtained by rotating point W by angle 2pi/3 about point M. Point A is the reflection of point M across point K. Point L is the reflection of point A across segment MW. Let N be the incenter of triangle ALW. Find the distance between points L and N. Express your answer as a d... | 13.33 | MATH |
[
{
"content": "Let EX = 1. Point G is obtained by rotating point E by angle 3pi/4 about point X. Let K be the reflection of point E across point G. Point M is the orthocenter of triangle XKG. Point B is the reflection of point E across point M. What is the distance between points B and K? Express your answer as ... | 13.51 | MATH |
[
{
"content": "Let ME = 11. Let Y be the rotation of point M by angle 11pi/12 around point E. Point T is the circumcenter of triangle MYE. Let I be the orthocenter of triangle MYE. Point J is the reflection of point T across segment EM. Point O is the midpoint of segment YE. Find the measure of angle OJI, in rad... | 229.59 | MATH |
[
{
"content": "WG = 10. Point Y is obtained by rotating point G by angle 7pi/12 about point W. Let I be the rotation of point W by angle 3pi/4 around point G. Point A is the reflection of point G across point I. Point O is the reflection of point A across segment GW. Let H be the midpoint of segment YI. Let X be... | 37.25 | MATH |
[
{
"content": "Let AF = 12. Let L be the rotation of point A by angle pi/4 around point F. Let J be the line through points L and F. Point C is the midpoint of segment AF. Line H is the reflection of line J across point A. Point R is the reflection of point L across line H. Point Y is the circumcenter of triangl... | 401.88 | MATH |
[
{
"content": "Let PR = 8. Let C be the rotation of point R by angle 5pi/6 around point P. Point W is the midpoint of segment CR. Point T is the midpoint of segment PC. Point M is the reflection of point T across segment PW. What is the length of segment MP? Express your answer as a decimal number rounded to 2 d... | 4.0 | MATH |
[
{
"content": "Let DU = 12. Point B is the reflection of point U across point D. Let Z be the rotation of point D by angle pi/12 around point B. Point S is the centroid of triangle ZUB. Let X be the incenter of triangle ZUB. Point W is the midpoint of segment XU. Find the measure of angle WSX, in radians. Expres... | 1.43 | MATH |
[
{
"content": "Let HE = 9. Let L be the rotation of point H by angle pi/4 around point E. Let V be the reflection of point E across point L. Point D is obtained by rotating point L by angle pi about point H. Let G be the midpoint of segment DV. Let P be the incenter of triangle LED. Let C be the reflection of po... | 7.17 | MATH |
[
{
"content": "Let AJ = 4. Line Z is the perpendicular bisector of segment JA. Point W lies on line Z at distance 8 from point J. Point F is the midpoint of segment AW. Point E is the reflection of point W across point J. Point S is the orthocenter of triangle FWE. What is the distance between points A and S? Ex... | 20.55 | MATH |
[
{
"content": "Let GP = 5. Line L is the perpendicular bisector of segment GP. Let A be the line through points G and P. Let H be the line through point G perpendicular to line A. Point T is the reflection of point P across point G. Let O be the rotation of point G by angle 5pi/6 around point P. Line E is the re... | 12.18 | MATH |
[
{
"content": "Let FR = 4. Let P be the vector from point R to point F. Point H is obtained by rotating point R by angle pi/4 about point F. Let Q be the angle bisector of angle HRF. Let Y be point H translated by vector P. Let K be the line through points H and Y. Line D is the reflection of line Q across point... | 7.9 | MATH |
[
{
"content": "OE = 11. L is placed 3 units away from E. Point Q is obtained by rotating point E by angle pi/3 about point L. Point U is obtained by rotating point L by angle 2pi/3 about point Q. Line G is the perpendicular bisector of segment EL. Point Z is the reflection of point U across line G. Let H be the ... | 7.5 | MATH |
[
{
"content": "Let X be the orthocenter of triangle B. Point F is the reflection of point Y across point B. Point D is the midpoint of segment XF. Point N is the reflection of point B across point D. What is the distance between points Y and N? Express your answer as a decimal number rounded to 2 decimal places.... | 1.15 | MATH |
[
{
"content": "Let LU = 2. Let J be the midpoint of segment UL. Point G is obtained by rotating point J by angle 11pi/12 about point L. Let H be the perpendicular bisector of segment GU. Line N is the reflection of line H across point G. Point Z is the reflection of point G across line N. Point M is the reflecti... | 0.13 | MATH |
[
{
"content": "Let LC = 5. Point Q is the midpoint of segment LC. Let D be the rotation of point C by angle pi/3 around point Q. Let S be the reflection of point Q across point D. Let W be the circumcenter of triangle DCS. Let Y be the circumcircle of triangle DCS. Let T be the reflection of circle Y through poi... | 7.02 | MATH |
[
{
"content": "KI = 11. Point A is obtained by rotating point I by angle 11pi/12 about point K. Let V be the reflection of point I across point A. Point F is the reflection of point A across point I. Point X is the orthocenter of triangle AKI. Let O be the perpendicular bisector of segment AX. Point D is the ref... | 103.55 | MATH |
[
{
"content": "Let HI = 2. Let V be the reflection of point I across point H. Let E be the reflection of point H across point I. Point J is obtained by rotating point V by angle 5pi/12 about point H. Point B is obtained by rotating point J by angle pi/3 about point V. Point C is the reflection of point J across ... | 2.6 | MATH |
[
{
"content": "WZ = 3. Point Q is obtained by rotating point Z by angle pi/2 about point W. Point L is the incenter of triangle QWZ. Circle E is the circumcircle of triangle QWZ. Let N be the reflection of point L across point Q. Let H be the inversion of point N in circle E. Find the length of segment NH. Expre... | 3.29 | MATH |
[
{
"content": "Let BP = 11. Let D be the rotation of point P by angle 11pi/12 around point B. Let A be the midpoint of segment PD. Circle G is the incircle of triangle DAB. Let C be the circumcenter of triangle DAB. Point E is the inversion of point P with respect to circle G. Line M passes through points E and ... | 1.2 | MATH |
[
{
"content": "Let RK = 10. Let S be the rotation of point R by angle 7pi/12 around point K. Let J be the incenter of triangle SKR. Let A be the centroid of triangle SKR. Point H is the midpoint of segment JR. Find the measure of angle RAH, in radians. Express your answer as a decimal number rounded to 2 decimal... | 1.32 | MATH |
[
{
"content": "Let EO = 5. Let L be the rotation of point O by angle pi/3 around point E. Let F be the reflection of point O across point L. Point Q is obtained by rotating point E by angle 7pi/12 about point O. Line A is the perpendicular bisector of segment OF. Point I is the reflection of point Q across line ... | 0.43 | MATH |
[
{
"content": "QN = 4. Point M is the midpoint of segment QN. Point G is obtained by rotating point Q by angle 2pi/3 about point M. Let H be the rotation of point N by angle 3pi/4 around point M. Point Z is the midpoint of segment MQ. Point J is the reflection of point G across segment MH. What is the inradius o... | 0.17 | MATH |
[
{
"content": "Let VO = 1. Line U passes through points O and V. Let X be the rotation of point V by angle pi/6 around point O. Line H passes through point X perpendicular to line U. Let F be the rotation of point X by angle 2pi/3 around point V. Let J be the line through point F perpendicular to line H. Point W... | 0.43 | MATH |
[
{
"content": "XV = 10. Point W is obtained by rotating point X by angle pi/6 about point V. Point R is the midpoint of segment WX. Let C be the orthocenter of triangle WXV. Point F is the reflection of point R across segment XV. Find the distance between points F and C. Express your answer as a decimal number r... | 4.87 | MATH |
[
{
"content": "YE = 2. Line N is the perpendicular bisector of segment EY. Let P be the reflection of point E across point Y. Point S lies on line N at distance 1 from point E. Point D is the midpoint of segment ES. Let L be the reflection of point E across point P. Point R is the midpoint of segment LD. Let J b... | 0.25 | MATH |
[
{
"content": "Let BV = 7. Let S be the rotation of point V by angle 5pi/12 around point B. Let M be the rotation of point B by angle 2pi/3 around point V. Point C is the centroid of triangle MBS. Point W is the orthocenter of triangle MBS. Point Q is the incenter of triangle MBS. Line H is the perpendicular bis... | 7.34 | MATH |
[
{
"content": "PB = 11. Line D is the perpendicular bisector of segment BP. Let Y be the midpoint of segment PB. Point V lies on line D at distance 5 from point Y. Let C be the reflection of line D through point B. Point U is the reflection of point P across line C. Let T be the midpoint of segment PU. Let J be ... | 4.03 | MATH |
[
{
"content": "Let QY = 7. Point E is the reflection of point Q across point Y. Point R is the reflection of point E across point Q. Line I is the perpendicular bisector of segment RQ. Point Z lies on line I at distance 9 from point Q. Let T be the reflection of point Z across point E. Point A is the midpoint of... | 74.81 | MATH |
[
{
"content": "FI = 10. Let V be the reflection of point I across point F. Let Y be the reflection of point F across point V. Let W be the rotation of point Y by angle 3pi/4 around point V. Point T is the reflection of point F across point Y. Let X be the midpoint of segment TW. Let S be the reflection of point ... | 0.91 | MATH |
[
{
"content": "VR = 10. Let W be the line through point R perpendicular to segment RV. Point Z is obtained by rotating point R by angle pi/4 about point V. Let P be the midpoint of segment ZR. Line A passes through point P parallel to line W. Point D is the midpoint of segment RV. Point H is the midpoint of segm... | 4.42 | MATH |
[
{
"content": "LS = 9. Let W be the rotation of point L by angle pi/2 around point S. Let M be the reflection of point W across point L. Let T be the centroid of triangle WLS. Point A is the reflection of point T across segment LS. What is the distance between points A and M? Express your answer as a decimal num... | 16.16 | MATH |
[
{
"content": "GP = 8. Point D is obtained by rotating point P by angle pi/12 about point G. Line J passes through points D and G. Point C is the reflection of point D across segment GP. Point W is the reflection of point P across line J. Let N be the midpoint of segment DP. What is the inradius of triangle CNG?... | 1.28 | MATH |
[
{
"content": "Point H is the midpoint of segment TI24. Let N be the midpoint of segment GH. Point I is the reflection of point G across point L. Point R is the midpoint of segment HI. Find the distance between points N and R. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the an... | 1.0 | MATH |
[
{
"content": "Let HW = 5. Let R be the rotation of point W by angle pi/3 around point H. Let X be the rotation of point R by angle 11pi/12 around point H. Point B is the midpoint of segment WX. Let M be the midpoint of segment XR. Point G is the reflection of point B across segment HX. Let P be the incenter of ... | 2.49 | MATH |
[
{
"content": "LS = 4. Let G be the midpoint of segment LS. Line X passes through point G perpendicular to segment LS. Let Z be the reflection of point S across point L. Let O be the reflection of point G across point S. Let H be the line through point S parallel to line X. Line T is the reflection of line X acr... | 1.13 | MATH |
[
{
"content": "Let OZ = 11. Line S is the perpendicular bisector of segment OZ. Point W is on line S with |WO| = 11. Point K is the circumcenter of triangle ZOW. Point J is the incenter of triangle ZOW. Point P is the reflection of point J across segment WZ. Find the distance between points K and P. Express your... | 6.68 | MATH |
[
{
"content": "Let NI = 2. Let A be the rotation of point I by angle pi/2 around point N. Point H is the midpoint of segment NA. Point K is the reflection of point H across point I. Let F be the perpendicular bisector of segment KH. Point R is the reflection of point N across line F. Point X is the centroid of t... | 1.74 | MATH |
[
{
"content": "CT = 9. Let V be the reflection of point C across point T. Let K be the midpoint of segment VT. Let S be the rotation of point V by angle 5pi/12 around point T. Point G is the orthocenter of triangle SKV. Let H be the midpoint of segment KV. Point L is the reflection of point G across point C. Let... | 47.53 | MATH |
[
{
"content": "Let SD = 8. Line Z is the perpendicular bisector of segment DS. Point E is on line Z with |ES| = 3. Line B passes through point S parallel to segment DE. Point C is the reflection of point D across line B. Point Q is the midpoint of segment ES. Find the length of segment CQ. Express your answer as... | 9.18 | MATH |
[
{
"content": "Let DP = 11. Point K is obtained by rotating point P by angle pi/6 about point D. Point Y is the reflection of point D across point K. Circle F is the incircle of triangle PKY. Let N be the inversion of point P in circle F. What is the distance between points D and N? Express your answer as a deci... | 12.26 | MATH |
[
{
"content": "Let HV = 3. Point R is obtained by rotating point V by angle pi/2 about point H. Point Z is obtained by rotating point V by angle pi/6 about point R. Let U be the midpoint of segment VZ. Point I is the reflection of point H across segment ZR. Let L be the midpoint of segment IZ. Find the measure o... | 4.2 | MATH |
[
{
"content": "IO = 9. Point P is obtained by rotating point O by angle 2pi/3 about point I. Point X is the circumcenter of triangle PIO. Point U is the incenter of triangle PIO. Point V is the reflection of point P across point U. Circle D is the circumcircle of triangle PIO. Let C be the inversion of point V i... | 4.72 | MATH |
[
{
"content": "Point Y is the midpoint of segment IA. Let L be the angle bisector of angle UIY. Point M is the circumcenter of triangle I. Point W is the midpoint of segment MU. Point O is the reflection of point W across point Y. Point X is the reflection of point O across line L. What is the length of segment ... | 1.23 | MATH |
[
{
"content": "EX = 4. Let B be the midpoint of segment EX. Line S is the perpendicular bisector of segment BX. Line M is the reflection of line S across point X. Point N is on line M with |NE| = 7. Point R is the reflection of point X across point N. Point D is the reflection of point E across segment NB. Find ... | 0.18 | MATH |
[
{
"content": "FQ = 6. Point K is the midpoint of segment QF. Let U be the rotation of point K by angle pi/12 around point F. Point Z is obtained by rotating point Q by angle 3pi/4 about point F. Let A be the reflection of point Q across point Z. Point B is the reflection of point A across segment UZ. Find the c... | 8.5 | MATH |
[
{
"content": "Let RV = 1. Let N be the perpendicular bisector of segment RV. Point C lies on line N at distance 10 from point V. Point P is the reflection of point C across point R. Let M be the midpoint of segment RP. Point T is the midpoint of segment PV. Let I be the incenter of triangle MPV. Point K is the ... | 7.54 | MATH |
[
{
"content": "Let TR = 4. Let W be the rotation of point T by angle pi around point R. Let X be the reflection of point R across point T. Let U be the midpoint of segment RW. Let V be the vector from point U to point R. Point M is obtained by rotating point X by angle pi/12 about point U. Let E be point X trans... | 1.97 | MATH |
[
{
"content": "CY = 6. Point S is obtained by rotating point C by angle 11pi/12 about point Y. Point H is obtained by rotating point C by angle 2pi/3 about point S. Point F is the orthocenter of triangle SCH. Let M be the line through point Y perpendicular to segment SC. Line Z passes through point S parallel to... | 11.9 | MATH |
[
{
"content": "QS = 3. Let H be the rotation of point S by angle 3pi/4 around point Q. Let V be the reflection of point S across point H. Let A be the incenter of triangle HVQ. Let K be the midpoint of segment QH. Find the distance between points K and A. Express your answer as a decimal number rounded to 2 deci... | 1.47 | MATH |
[
{
"content": "WD = 12. Let P be the rotation of point D by angle 2pi/3 around point W. Line H is the angle bisector of angle DPW. Point T is the reflection of point W across line H. Let Y be the midpoint of segment DW. What is the inradius of triangle PTY? Express your answer as a decimal number rounded to 2 de... | 1.11 | MATH |
[
{
"content": "AX = 3. Point J is the reflection of point A across point X. Line N is the angle bisector of angle AJX. Let U be the rotation of point J by angle pi/4 around point X. Point H is the reflection of point U across line N. Point O is the midpoint of segment HU. Point I is the reflection of point J acr... | 1.86 | MATH |
[
{
"content": "Let IT = 11. Point C is the midpoint of segment TI. Let B be the rotation of point C by angle pi/12 around point I. Let H be the rotation of point T by angle 11pi/12 around point B. Let P be the rotation of point B by angle 11pi/12 around point C. Let W be the angle bisector of angle CPH. Point L ... | 0.52 | MATH |
[
{
"content": "ZF = 4. Let X be the reflection of point F across point Z. Point O is obtained by rotating point Z by angle pi/3 about point F. Point E is the centroid of triangle OXZ. Let C be the perpendicular bisector of segment EO. Point K is the reflection of point Z across line C. What is the distance betwe... | 1.33 | MATH |
[
{
"content": "Point R is the orthocenter of triangle J. Let Y be the circumcircle of triangle J. Circle T is the reflection of circle Y across point P. Let G be the inversion of point P in circle T. Find the length of segment RG. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent th... | 0.95 | MATH |
[
{
"content": "Let TY = 1. Point U is the midpoint of segment YT. Let H be the rotation of point U by angle pi/12 around point Y. Point B is obtained by rotating point Y by angle pi/6 about point H. Let G be the rotation of point T by angle pi/2 around point U. Point L is the centroid of triangle TYB. Let J be t... | 0.36 | MATH |
[
{
"content": "Let MV = 8. Let S be the rotation of point M by angle pi/6 around point V. Point J is obtained by rotating point V by angle pi about point M. Line N is the perpendicular bisector of segment VS. Point U is the reflection of point M across line N. Let P be the centroid of triangle MSU. What is the d... | 10.05 | MATH |
[
{
"content": "UR = 6. Point E is obtained by rotating point U by angle 5pi/12 about point R. Let G be the rotation of point U by angle pi/4 around point R. Point F is the reflection of point G across point E. Let W be the reflection of point U across point E. Let M be the orthocenter of triangle GFR. What is th... | 9.23 | MATH |
[
{
"content": "Let DZ = 8. Let K be the rotation of point Z by angle 3pi/4 around point D. Let P be the reflection of point Z across point K. Let I be the reflection of point K across point D. Line A passes through point Z parallel to segment KI. Line B passes through point P parallel to segment IZ. Let O be the... | 21.94 | MATH |
[
{
"content": "BH = 2. Let F be the rotation of point B by angle 11pi/12 around point H. Let Y be the rotation of point H by angle 11pi/12 around point B. Point G is the reflection of point Y across point B. Point E is the midpoint of segment HF. Point U is the reflection of point G across segment HF. Point I is... | 2.46 | MATH |
[
{
"content": "MF = 6. Let K be the reflection of point F across point M. Line G passes through point K perpendicular to segment FM. Point Q lies on line G. S is constructed so that QS = 9. Point O lies on line G. Point E is the reflection of point O across segment FM. Let V be the midpoint of segment SE. Let T ... | 4.5 | MATH |
[
{
"content": "NX = 1. Let D be the rotation of point X by angle 3pi/4 around point N. Point P is obtained by rotating point X by angle pi/4 about point N. Let I be the midpoint of segment XD. Point M is the circumcenter of triangle NIP. Point B is the orthocenter of triangle NIP. Find the length of segment MB. ... | 1.51 | MATH |
[
{
"content": "Let PM = 9. Point H is obtained by rotating point M by angle 2pi/3 about point P. Point W is the reflection of point H across point M. Point E is the incenter of triangle HMP. Point X is the reflection of point W across segment PH. What is the distance between points E and X? Express your answer a... | 26.1 | MATH |
[
{
"content": "Let MA = 11. Let R be the vector from point A to point M. Point U is obtained by rotating point A by angle 7pi/12 about point M. Point D is the translation of point M by vector R. Let K be the line through point U perpendicular to segment UM. Let Z be the circumcenter of triangle AUM. Let Y be the... | 1.31 | MATH |
[
{
"content": "XW = 3. Point J is the reflection of point X across point W. Let H be the midpoint of segment WX. Let S be the midpoint of segment HJ. Point F is obtained by rotating point X by angle pi/2 about point W. Let Q be the angle bisector of angle HFS. Let G be the reflection of point F across point X. L... | 6.21 | MATH |
[
{
"content": "Let VQ = 4. Let J be the perpendicular bisector of segment QV. Point W lies on line J. Let S be the midpoint of segment QW. Let X be the line through point Q parallel to line J. Point L is the reflection of point V across line X. Point D is the reflection of point V across point S. Point Z is the ... | 4.0 | MATH |
[
{
"content": "Let HD = 7. Point V is obtained by rotating point D by angle pi/6 about point H. Point E is obtained by rotating point D by angle 5pi/12 about point V. Let I be the reflection of point H across point V. Let M be the circumcenter of triangle HDE. Point S is the midpoint of segment HD. What is the c... | 26.43 | MATH |
[
{
"content": "Let RW = 11. Point E is the midpoint of segment RW. Let Q be the rotation of point E by angle 2pi/3 around point R. Point L is the orthocenter of triangle WEQ. Let Y be the reflection of point R across point L. Let O be the midpoint of segment LW. Let P be the centroid of triangle WYL. What is the... | 12.33 | MATH |
[
{
"content": "IG = 1. Let N be the reflection of point G across point I. Let R be the line through points G and I. Let Q be the rotation of point N by angle pi around point G. Let J be the reflection of point I across point G. Point C is obtained by rotating point Q by angle 5pi/12 about point J. Line H is the ... | 2.04 | MATH |
[
{
"content": "Let IL = 4. Point R is the reflection of point L across point I. Let G be the rotation of point R by angle pi/2 around point L. Point P is the centroid of triangle IGL. Point V is the incenter of triangle IGL. Point J is the reflection of point V across point I. What is the measure of angle JVP, i... | 2.52 | MATH |
[
{
"content": "Let GB = 6. Point F is the midpoint of segment BG. Line Z is the perpendicular bisector of segment FB. Point U is the reflection of point F across point G. Point A is obtained by rotating point F by angle pi/12 about point U. Point H is the reflection of point U across line Z. Point Q is the refle... | 5.43 | MATH |
[
{
"content": "BT = 1. Let D be the reflection of point T across point B. Point K is the midpoint of segment BD. Point X is obtained by rotating point K by angle 2pi/3 about point B. Let Q be the reflection of point X across point T. Point O is the orthocenter of triangle QXD. Let W be the midpoint of segment DQ... | 0.09 | MATH |
[
{
"content": "HD = 7. Let P be the line through points H and D. Let K be the rotation of point H by angle pi/4 around point D. Line Y passes through point K perpendicular to line P. Point F is obtained by rotating point H by angle 5pi/12 about point K. Point V is the reflection of point D across line Y. Point W... | 0.69 | MATH |
[
{
"content": "VN = 5. Point C is the midpoint of segment VN. Let R be the rotation of point C by angle pi/4 around point V. Point O is the reflection of point N across segment RC. Point U is the reflection of point R across point C. Find the inradius of triangle OUN. Express your answer as a decimal number roun... | 0.46 | MATH |
[
{
"content": "Let IB = 5. Point U is obtained by rotating point I by angle 5pi/6 about point B. Let V be the centroid of triangle UIB. Point S is the midpoint of segment IB. Let M be the incircle of triangle UIB. Point E is the inversion of point S with respect to circle M. What is the distance between points E... | 0.26 | MATH |
[
{
"content": "Let OQ = 5. Point K is the midpoint of segment OQ. Let R be the rotation of point K by angle 5pi/6 around point O. Let W be the rotation of point O by angle 5pi/12 around point R. Let Y be the incircle of triangle WOR. Let E be the midpoint of segment OR. Point J is the reflection of point K acros... | 0.01 | MATH |
[
{
"content": "Let QF = 5. Z is placed 4 units away from F. Point P is obtained by rotating point F by angle 11pi/12 about point Q. Let U be the midpoint of segment PF. Let O be the midpoint of segment QZ. Point Y is the midpoint of segment ZU. What is the length of segment OY? Express your answer as a decimal n... | 0.33 | MATH |
[
{
"content": "BV = 1. Point E is the midpoint of segment BV. Let W be the rotation of point E by angle pi/2 around point B. Point K is obtained by rotating point V by angle 5pi/12 about point E. Circle G is the incircle of triangle KBW. Point F is the inversion of point B with respect to circle G. Let T be the ... | 0.27 | MATH |
[
{
"content": "JN = 12. Let Y be the rotation of point N by angle 7pi/12 around point J. Let Z be the reflection of point Y across point J. Let G be the centroid of triangle YJN. Let H be the midpoint of segment NG. Point B is the midpoint of segment JG. What is the inradius of triangle ZHB? Express your answer ... | 2.4 | MATH |
[
{
"content": "Let RH = 9. Point W is the midpoint of segment RH. Point B is obtained by rotating point W by angle pi/4 about point R. Line X is the angle bisector of angle WBR. Let G be the reflection of line X through point R. Point J is the reflection of point W across line G. Point U is the reflection of poi... | 28.8 | MATH |
[
{
"content": "MP = 12. Let H be the line through points P and M. Let T be the rotation of point M by angle pi/3 around point P. Point L is the reflection of point T across line H. Let V be the reflection of point M across point L. Let Z be the orthocenter of triangle MTV. What is the length of segment VZ? Expre... | 34.64 | MATH |
[
{
"content": "RK = 9. Let A be the rotation of point R by angle pi/4 around point K. Let W be the line through points A and R. Point M is obtained by rotating point K by angle 11pi/12 about point R. Point P is the reflection of point M across line W. Point X is the reflection of point A across segment RK. Let J... | 0.43 | MATH |
[
{
"content": "Let WZ = 4. Let O be the reflection of point Z across point W. Let K be the rotation of point Z by angle 7pi/12 around point W. Let X be the perpendicular bisector of segment OW. Let D be the circumcenter of triangle KWO. Point A is the reflection of point D across line X. Let E be the midpoint of... | 2.58 | MATH |
[
{
"content": "Let EB = 12. Line U is the perpendicular bisector of segment EB. Point T is obtained by rotating point B by angle 11pi/12 about point E. Let A be the line through point B parallel to line U. Line P is the reflection of line A across line U. Point D is the reflection of point B across line P. Point... | 12.18 | MATH |
[
{
"content": "Let EH = 7. Point M is obtained by rotating point E by angle 2pi/3 about point H. Point J is the reflection of point H across point E. Let O be the perpendicular bisector of segment HM. Point B is the reflection of point J across line O. Let W be the reflection of point J across point B. Find the ... | 42.44 | MATH |
[
{
"content": "IY = 7. Point H is obtained by rotating point I by angle 5pi/12 about point Y. Point C is the midpoint of segment IH. Let U be the midpoint of segment YI. Point L is the centroid of triangle HYI. Let N be the midpoint of segment LU. Point Z is the reflection of point Y across point N. Find the dis... | 2.32 | MATH |
[
{
"content": "QL = 3. Let S be the rotation of point Q by angle pi/3 around point L. I is constructed so that LI = 12. Point K is the midpoint of segment IQ. Point U is the midpoint of segment KL. Let F be the circumcenter of triangle KUS. Find the length of segment FU. Express your answer as a decimal number r... | 1.0 | MATH |
[
{
"content": "Let FX = 9. Let T be the rotation of point X by angle pi/2 around point F. Let C be the circumcenter of triangle XFT. Let Y be the midpoint of segment XC. Point J is the reflection of point T across point X. What is the distance between points Y and J? Express your answer as a decimal number round... | 15.95 | MATH |
[
{
"content": "AT = 8. Let S be the perpendicular bisector of segment AT. Point K lies on line S at distance 12 from point A. Point Y is the incenter of triangle KAT. Let W be the circumcenter of triangle KAT. Point F is the midpoint of segment AY. What is the distance between points W and F? Express your answer... | 3.25 | MATH |
[
{
"content": "Let TE = 10. Let Y be the midpoint of segment TE. Point S is obtained by rotating point Y by angle 11pi/12 about point T. Let U be the midpoint of segment SE. Let N be the reflection of point T across point S. Point J is the reflection of point U across point Y. Point F is the reflection of point ... | 17.35 | MATH |
[
{
"content": "Let UC = 2. Point L is obtained by rotating point U by angle 2pi/3 about point C. Point P is the centroid of triangle LUC. Let N be the circumcircle of triangle LUC. Let I be the inversion of point P in circle N. What is the distance between points I and U? Express your answer as a decimal number ... | 2.65 | MATH |
[
{
"content": "JL = 12. Point O is obtained by rotating point J by angle 2pi/3 about point L. Let D be the reflection of point O across point J. Let N be the circumcenter of triangle OJL. Find the inradius of triangle DLN. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer... | 1.86 | MATH |
[
{
"content": "Let RU = 6. Let H be the midpoint of segment UR. Point C is obtained by rotating point R by angle pi/2 about point H. Point T is the reflection of point C across segment UR. Point K is the reflection of point R across point U. Let Y be the reflection of point T across point K. Let O be the midpoin... | 0.94 | MATH |
[
{
"content": "DY = 9. Point L is the midpoint of segment DY. Let G be the rotation of point L by angle 7pi/12 around point Y. Point C is the reflection of point G across point D. Point V is the reflection of point C across segment LD. Point M is the midpoint of segment CD. Find the inradius of triangle MLV. Exp... | 2.2 | MATH |
[
{
"content": "Let LU = 6. Let X be the rotation of point L by angle pi/12 around point U. Let Y be the rotation of point L by angle pi/6 around point U. Let K be the midpoint of segment YL. Point C is the midpoint of segment XY. Let R be the midpoint of segment LX. What is the measure of angle CRK, in radians? ... | 0.08 | MATH |
[
{
"content": "XS = 10. Point E is the midpoint of segment XS. Let I be the rotation of point S by angle pi/12 around point E. Let Y be the perpendicular bisector of segment SX. Point B is the reflection of point I across line Y. Let Q be the circumcenter of triangle EXI. Let V be the orthocenter of triangle XBQ... | 1.07 | MATH |
[
{
"content": "Let CO = 4. Let A be the rotation of point O by angle 7pi/12 around point C. Let Q be the incenter of triangle OAC. Let N be the reflection of point Q across point O. Point X is the orthocenter of triangle OAC. What is the length of segment NX? Express your answer as a decimal number rounded to 2 ... | 8.21 | MATH |
[
{
"content": "Let HT = 8. Let M be the rotation of point H by angle 11pi/12 around point T. Point J is the midpoint of segment TM. Let I be the line through points H and J. Let B be the reflection of line I through point T. Line D passes through point J perpendicular to line I. Line P passes through point T par... | 13.79 | MATH |
[
{
"content": "OB = 5. Line L is the perpendicular bisector of segment OB. Point N is obtained by rotating point B by angle 11pi/12 about point O. Let A be the rotation of point N by angle 7pi/12 around point B. Point T is obtained by rotating point A by angle pi/4 about point N. Point S is the reflection of poi... | 19.92 | MATH |
[
{
"content": "DY = 2. Let Q be the rotation of point D by angle pi/6 around point Y. Point N is the midpoint of segment YQ. Point K is the midpoint of segment NY. Point A is the reflection of point Y across point D. Let W be the midpoint of segment KD. What is the measure of angle WDA, in radians? Express your ... | 0.12 | MATH |
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