{"status": "success", "data": {"description_md": "In triangle $ABC,$ point $D$ is on $\\overline{BC}$ with $CD=2$ and $DB=5,$ point $E$ is on $\\overline{AC}$ with $CE=1$ and $EA=3,$ $AB=8,$ and $\\overline{AD}$ and $\\overline{BE}$ intersect at $P.$ Points $Q$ and $R$ lie on $\\overline{AB}$ so that $\\overline{PQ}$ is parallel to $\\overline{CA}$ and $\\overline{PR}$ is parallel to $\\overline{CB}.$ It is given that the ratio of the area of triangle $PQR$ to the area of triangle $ABC$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "

In triangle ABC, point D is on \\overline{BC} with CD=2 and DB=5, point E is on \\overline{AC} with CE=1 and EA=3, AB=8, and \\overline{AD} and \\overline{BE} intersect at P. Points Q and R lie on \\overline{AB} so that \\overline{PQ} is parallel to \\overline{CA} and \\overline{PR} is parallel to \\overline{CB}. It is given that the ratio of the area of triangle PQR to the area of triangle ABC is m/n, where m and n are relatively prime positive integers. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2002 AIME II Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_II_p14", "prev": "/problem/02_aime_II_p12"}}