{"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":"06190a0a-f16f-565b-8e61-fe40611d6dd6","task_key":"test--06190a0a-f16f-565b-8e61-fe40611d6dd6","task_revision_id":"1","upstream_id":"","short_description":"(Self-Isogonal Cubics) Let $A B C$ be a triangle with $A B=2, A C=3, B C=4$. The…","config":"","split":"test","body":"{\"problem\":\"(Self-Isogonal Cubics) Let $A B C$ be a triangle with $A B=2, A C=3, B C=4$. The isogonal conjugate of a point $P$, denoted $P^{*}$, is the point obtained by intersecting the reflection of lines $P A$, $P B, P C$ across the angle bisectors of $\\\\angle A, \\\\angle B$, and $\\\\angle C$, respectively. Given a point $Q$, let $\\\\mathfrak{K}(Q)$ denote the unique cubic plane curve which passes through all points $P$ such that line $P P^{*}$ contains $Q$. Consider: (a) the M'Cay cubic $\\\\mathfrak{K}(O)$, where $O$ is the circumcenter of $\\\\triangle A B C$, (b) the Thomson cubic $\\\\mathfrak{K}(G)$, where $G$ is the centroid of $\\\\triangle A B C$, (c) the Napoleon-Feurerbach cubic $\\\\mathfrak{K}(N)$, where $N$ is the nine-point center of $\\\\triangle A B C$, (d) the Darboux cubic $\\\\mathfrak{K}(L)$, where $L$ is the de Longchamps point (the reflection of the orthocenter across point $O)$ (e) the Neuberg cubic $\\\\mathfrak{K}\\\\left(X_{30}\\\\right)$, where $X_{30}$ is the point at infinity along line $O G$, (f) the nine-point circle of $\\\\triangle A B C$, (g) the incircle of $\\\\triangle A B C$, and (h) the circumcircle of $\\\\triangle A B C$. Estimate $N$, the number of points lying on at least two of these eight curves.\"}","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":[]}