{"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":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"98408fe4-5091-57dd-b763-d5f8f5079328","task_key":"test--98408fe4-5091-57dd-b763-d5f8f5079328","task_revision_id":"1","upstream_id":"","short_description":"Let $A B C$ be a triangle that satisfies $A B=13, B C=14, A C=15$. Given a point…","config":"","split":"test","body":"{\"problem\":\"Let $A B C$ be a triangle that satisfies $A B=13, B C=14, A C=15$. Given a point $P$ in the plane, let $P_{A}, P_{B}, P_{C}$ be the reflections of $A, B, C$ across $P$. Call $P$ good if the circumcircle of $P_{A} P_{B} P_{C}$ intersects the circumcircle of $A B C$ at exactly 1 point. The locus of good points $P$ encloses a region $\\\\mathcal{S}$. Find the area of $\\\\mathcal{S}$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}