{"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":"a31fd718-8df1-581a-85c0-368d87dbb980","task_key":"geometry--test--a31fd718-8df1-581a-85c0-368d87dbb980","task_revision_id":"1","upstream_id":"","short_description":"In $\\triangle ABC$, $AB = 13$, $AC=5$ and $BC=12$. Points $M$ and $N$ lie on…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In $\\\\triangle ABC$, $AB = 13$, $AC=5$ and $BC=12$.  Points $M$ and $N$ lie on $\\\\overline{AC}$ and $\\\\overline{BC}$, respectively, with $CM = CN = 4$. Points $J$ and $K$ are on $\\\\overline{AB}$ so that $\\\\overline{MJ}$ and $\\\\overline{NK}$ are perpendicular to $\\\\overline{AB}$. What is the area of pentagon $CMJKN$? Express your answer as a common fraction.\\n\\n[asy]\\npair A,B,C,N,K,M,J;\\nA=(0,5);\\nB=(12,0);\\nC=(0,0);\\nN=(5,0);\\nM=(0,4);\\nJ=(0.35,4.84);\\nK=(6,2.4);\\ndraw(A--B--C--cycle,linewidth(0.7));\\ndraw(N--K,linewidth(0.7));\\ndraw(M--J,linewidth(0.7));\\nlabel(\\\"$A$\\\",A,NW);\\nlabel(\\\"$M$\\\",M,W);\\nlabel(\\\"$C$\\\",C,SW);\\nlabel(\\\"$N$\\\",N,S);\\nlabel(\\\"$B$\\\",B,SE);\\nlabel(\\\"$K$\\\",K,NE);\\nlabel(\\\"$J$\\\",J,NE);\\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":[]}