{"status": "success", "data": {"description_md": "In triangle $ ABC$ the medians $ \\overline{AD}$ and $ \\overline{CE}$ have lengths 18 and 27, respectively, and $ AB = 24$. Extend $ \\overline{CE}$ to intersect the circumcircle of $ ABC$ at $ F$. The area of triangle $ AFB$ is $ m\\sqrt {n}$, where $ m$ and $ n$ are positive integers and $ n$ is not divisible by the square of any prime. 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": "<p>In triangle $ ABC$ the medians $ \\overline{AD}$ and $ \\overline{CE}$ have lengths 18 and 27, respectively, and $ AB = 24$. Extend $ \\overline{CE}$ to intersect the circumcircle of $ ABC$ at $ F$. The area of triangle $ AFB$ is $ m\\sqrt {n}$, where $ m$ and $ n$ are positive integers and $ n$ is not divisible by the square of any prime. Find $ m + n$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2002 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_I_p14", "prev": "/problem/02_aime_I_p12"}}