{"status": "success", "data": {"description_md": "Point $P$ is inside $\\triangle ABC$. Line segments $APD$, $BPE$, and $CPF$ are drawn with $D$ on $BC$, $E$ on $AC$, and $F$ on $AB$ (see the figure at right). Given that $AP=6$, $BP=9$, $PD=6$, $PE=3$, and $CF=20$, find the area of $\\triangle ABC$.

$\\includegraphics[width=87, height=167, totalheight=167]{https://latex.artofproblemsolving.com/4/4/a/44a05b204faea03b1943369da6171637ce3c71c0.png}$\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": "

Point P is inside \\triangle ABC. Line segments APD, BPE, and CPF are drawn with D on BC, E on AC, and F on AB (see the figure at right). Given that AP=6, BP=9, PD=6, PE=3, and CF=20, find the area of \\triangle ABC.

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": "1989 AIME Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/89_aime_p14"}}