{"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":"5c1152ce-c032-55df-86fb-1c86380e9562","task_key":"geometry--test--5c1152ce-c032-55df-86fb-1c86380e9562","task_revision_id":"1","upstream_id":"","short_description":"Five points $A$, $B$, $C$, $D$, and $O$ lie on a flat field. $A$ is directly…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Five points $A$, $B$, $C$, $D$, and $O$ lie on a flat field.  $A$ is directly north of $O$, $B$ is directly west of $O$, $C$ is directly south of $O$, and $D$ is directly east of $O$. The  distance between $C$ and $D$ is 140 m.  A hot-air balloon is positioned in the air at $H$ directly above $O$. The balloon is held in place by four ropes $HA$, $HB$, $HC$, and $HD$.  Rope $HC$ has length 150 m and rope $HD$ has length 130 m. [asy]\\nsize(250);\\npair A, B, C, D, O, H, W, X, Y, Z;\\nO=(0,0);\\nA=(1,1);\\nD=(1.5,-.3);\\nB=(-1.5,.3);\\nC=(-1,-1);\\nH=(0,2.5);\\nW=(5/3)*(A+D);\\nX=(5/3)*(A+B);\\nY=(-1)*(W);\\nZ=(-1)*(X);\\ndraw(W--X--Y--Z--W);\\ndraw(A--C);\\ndraw(B--D);\\ndraw(O--H, linewidth(1));\\ndraw(A--H, dashed);\\ndraw(B--H, dashed);\\ndraw(C--H, dashed);\\ndraw(D--H, dashed);\\ndot(A);\\ndot(B);\\ndot(C);\\ndot(D);\\ndot(O);\\ndot(H);\\nlabel(\\\"A\\\", A, NE);\\nlabel(\\\"B\\\", B, SW);\\nlabel(\\\"C\\\", C, SE);\\nlabel(\\\"D\\\", D, NE);\\nlabel(\\\"O\\\", O, SE);\\nlabel(\\\"H\\\", H, NW);\\n[/asy]\\n\\nTo reduce the total length of rope used, rope $HC$ and rope $HD$ are to be replaced by a single rope $HP$ where $P$ is a point on the straight line between $C$ and $D$. (The balloon remains at the same position $H$ above $O$ as described above.)  Determine the greatest length of rope that can be saved.\",\"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":[]}