{"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":"a1ab67ed-56af-5e0b-8b21-872f7e7ad6a9","task_key":"test--a1ab67ed-56af-5e0b-8b21-872f7e7ad6a9","task_revision_id":"1","upstream_id":"","short_description":"Let ${\\cal C}_1$ and ${\\cal C}_2$ be concentric circles, with ${\\cal C}_2$ in…","config":"","split":"test","body":"{\"problem\":\"Let ${\\\\cal C}_1$ and ${\\\\cal C}_2$ be  concentric circles, with ${\\\\cal C}_2$ in the interior of ${\\\\cal C}_1$ . From a point $A$ on ${\\\\cal C}_1$ one draws the tangent $AB$ to ${\\\\cal C}_2$ ( $B\\\\in {\\\\cal C}_2$ ). Let $C$ be the second point of intersection of $AB$ and ${\\\\cal C}_1$ , and let $D$ be the midpoint of $AB$ . A line passing through $A$ intersects ${\\\\cal C}_2$ at $E$ and $F$ in such a way that the perpendicular  bisectors of $DE$ and $CF$ intersect at a point $M$ on $AB$ . Find, with proof,  the ratio $AM/MC$ .\"}","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":[]}