{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"aime-2024","formal_name":"AIME 2024","introduction":"The 30 problems of the 2024 American Invitational Mathematics Examination (AIME I and II). Every answer is an integer from 0 to 999, with no options and no partial credit. It is a frequent reference point for reasoning models.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/Maxwell-Jia/AIME_2024","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"cedfddc6-965b-5cbd-bddd-0a83e0fb41c3","task_key":"default--train--cedfddc6-965b-5cbd-bddd-0a83e0fb41c3","task_revision_id":"2","upstream_id":"","short_description":"AIME 2024 train cedfddc6-965b-5cbd-bddd-0a83e0fb41c3","config":"default","split":"train","body":"{\"Problem\":\"Let $ABC$ be a triangle inscribed in circle $\\\\omega$. Let the tangents to $\\\\omega$ at $B$ and $C$ intersect at point $D$, and let $\\\\overline{AD}$ intersect $\\\\omega$ at $P$. If $AB=5$, $BC=9$, and $AC=10$, $AP$ can be written as the form $\\\\frac{m}{n}$, where $m$ and $n$ are relatively prime integers. Find $m + n$.\\n\\n[asy] import olympiad;  unitsize(15);  pair A, B, C, D, E, F, P, O;  C = origin; A = (10,0); B = (7.8, 4.4899); draw(A--B--C--cycle); draw(A..B..C..cycle, red+dotted);  O = circumcenter(A, B, C);  E = rotate(90,B) * (O); F = rotate(90,C) * (O);  D = IP(B..E + (B-E)*4, C..F + (C-F)*-3);  draw(B--D--C--D--A);  P = IP(D..A, A..B..C);  dot(A); dot(B); dot(C); dot(D); dot(P); label(\\\"$A$\\\", A, dir(335)); label(\\\"$B$\\\", B, dir(65)); label(\\\"$C$\\\", C, dir(200)); label(\\\"$D$\\\", D, dir(135)); label(\\\"$P$\\\", P, dir(235)); [/asy]\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/Maxwell-Jia/AIME_2024","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}