{"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":"10aa1b38-29c7-5139-9896-ec9a5fc08f40","task_key":"geometry--test--10aa1b38-29c7-5139-9896-ec9a5fc08f40","task_revision_id":"1","upstream_id":"","short_description":"In rectangle $ABCD$, we have $AB=8$, $BC=9$, $H$ is on $\\overline{BC}$ with…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"In rectangle $ABCD$, we have $AB=8$, $BC=9$, $H$ is on $\\\\overline{BC}$ with $BH=6$, $E$ is on $AD$ with $DE=4$, line $EC$ intersects line $AH$ at $G$, and $F$ is on line $AD$ with $\\\\overline{GF}\\\\perp \\\\overline{AF}$. Find the length $\\\\overline{GF}$.\\n\\n[asy]\\npair A,B,C,D,I,F,G,H;\\nF=(0,0);\\nD=(6,0);\\nI=(10,0);\\nA=(15,0);\\nB=(15,8);\\nH=(9,8);\\nC=(6,8);\\nG=(0,20);\\ndraw(A--B--C--D--cycle,linewidth(0.7));\\ndraw(A--F--G--cycle,linewidth(0.7));\\ndraw(G--I,linewidth(0.7));\\nlabel(\\\"4\\\",(8,0),S);\\nlabel(\\\"8\\\",(15,4),E);\\nlabel(\\\"6\\\",(12,8),N);\\nlabel(\\\"$A$\\\",A,SE);\\nlabel(\\\"$B$\\\",B,NE);\\nlabel(\\\"$C$\\\",C,W);\\nlabel(\\\"$D$\\\",D,S);\\nlabel(\\\"$E$\\\",I,S);\\nlabel(\\\"$F$\\\",F,W);\\nlabel(\\\"$G$\\\",G,W);\\nlabel(\\\"$H$\\\",H,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":[]}