{"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":"ee287752-0d94-5f70-aa30-078eda3156ee","task_key":"test--ee287752-0d94-5f70-aa30-078eda3156ee","task_revision_id":"1","upstream_id":"","short_description":"Suppose we have an (infinite) cone $\\mathcal{C}$ with apex $A$ and a plane…","config":"","split":"test","body":"{\"problem\":\"Suppose we have an (infinite) cone $\\\\mathcal{C}$ with apex $A$ and a plane $\\\\pi$. The intersection of $\\\\pi$ and $\\\\mathcal{C}$ is an ellipse $\\\\mathcal{E}$ with major axis $BC$, such that $B$ is closer to $A$ than $C$, and $BC=4, AC=5, AB=3$. Suppose we inscribe a sphere in each part of $\\\\mathcal{C}$ cut up by $\\\\mathcal{E}$ with both spheres tangent to $\\\\mathcal{E}$. What is the ratio of the radii of the spheres (smaller to larger)?\"}","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":[]}