{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/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":"4739d646-ed3c-5370-a83d-1f37ef4a1404","task_key":"geometry--test--4739d646-ed3c-5370-a83d-1f37ef4a1404","task_revision_id":"1","upstream_id":"","short_description":"Square $ABCD$ has side length $s$, a circle centered at $E$ has radius $r$, and…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Square $ABCD$ has side length $s$, a circle centered at $E$ has radius $r$, and $r$ and $s$ are both rational. The circle passes through $D$, and $D$ lies on $\\\\overline{BE}$. Point $F$ lies on the circle, on the same side of $\\\\overline{BE}$ as $A$. Segment $AF$ is tangent to the circle, and $AF=\\\\sqrt{9+5\\\\sqrt{2}}$. What is $r/s$?\\n\\n[asy]\\npair A,B,C,D,I,F;\\nA=(0,10); B=(0,0); C=(10,0); D=(10,10);\\n\\nI=(14,13); F=(11,17);\\ndraw(A--B--C--D--cycle,linewidth(0.7));\\ndraw(Circle(I,5),linewidth(0.7));\\ndraw(A--F,linewidth(0.7));\\nlabel(\\\"$A$\\\",A,NW);\\nlabel(\\\"$B$\\\",B,SW);\\nlabel(\\\"$C$\\\",C,SE);\\nlabel(\\\"$D$\\\",D,SW);\\nlabel(\\\"$F$\\\",F,N);\\nlabel(\\\"$E$\\\",I,E);\\ndot(I);\\n[/asy]\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}