{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"a90719d7-245e-5e63-9d8a-dcf90d2d7aaa","task_key":"test--a90719d7-245e-5e63-9d8a-dcf90d2d7aaa","task_revision_id":"4","upstream_id":"","short_description":"Points $A$, $V_1$, $V_2$, $B$, $U_2$, $U_1$ lie fixed on a circle $\\Gamma$, in…","config":"","split":"test","body":"{\"problem\":\"Points $A$, $V_1$, $V_2$, $B$, $U_2$, $U_1$ lie fixed on a circle $\\\\Gamma$, in that order, and such that $BU_2 > AU_1 > BV_2 > AV_1$.\\n\\nLet $X$ be a variable point on the arc $V_1 V_2$ of $\\\\Gamma$ not containing $A$ or $B$.  Line $XA$ meets line $U_1 V_1$ at $C$, while line $XB$ meets line $U_2 V_2$ at $D$.  Let $O$ and $\\\\rho$ denote the circumcenter and circumradius of $\\\\triangle XCD$, respectively.\\n\\nProve there exists a fixed point $K$ and a real number $c$, independent of $X$, for which $OK^2 - \\\\rho^2 = c$ always holds regardless of the choice of $X$.\"}","display_format":"text","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}