{"status": "success", "data": {"description_md": "In $\\triangle ABC$, $AB = 360$, $BC = 507$, and $CA = 780$. Let $M$ be the midpoint of $\\overline{CA}$, and let $D$ be the point on $\\overline{CA}$ such that $\\overline{BD}$ bisects angle $ABC$. Let $F$ be the point on $\\overline{BC}$ such that $\\overline{DF} \\perp \\overline{BD}$. Suppose that $\\overline{DF}$ meets $\\overline{BM}$ at $E$. The ratio $DE: EF$ can be written in the form $m/n$, 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, AB = 360, BC = 507, and CA = 780. Let M be the midpoint of \\overline{CA}, and let D be the point on \\overline{CA} such that \\overline{BD} bisects angle ABC. Let F be the point on \\overline{BC} such that \\overline{DF} \\perp \\overline{BD}. Suppose that \\overline{DF} meets \\overline{BM} at E. The ratio DE: EF can be written in the form 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": "2003 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/03_aime_I_p14"}}