{"status": "success", "data": {"description_md": "Let $ABCD$ be a parallelogram with $\\angle BAD < 90^{\\circ}$. A circle tangent to sides $\\overline{DA}$, $\\overline{AB}$, and $\\overline{BC}$ intersects diagonal $\\overline{AC}$ at points $P$ and $Q$ with $AP < AQ$, as shown. Suppose that $AP = 3$, $PQ = 9$, and $QC = 16$. Then the area of $ABCD$ can be expressed in the form $m\\sqrt n$, where $m$ and $n$ are positive integers, and $n$ is not divisible by the square of any prime. Find $m+n$.

$\\includegraphics[width=189, height=104, totalheight=104]{https://latex.artofproblemsolving.com/9/4/7/9471215d85465568eba3e615c0538a62e755bcf8.png}$\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": "

Let ABCD be a parallelogram with \\angle BAD < 90^{\\circ}. A circle tangent to sides \\overline{DA}, \\overline{AB}, and \\overline{BC} intersects diagonal \\overline{AC} at points P and Q with AP < AQ, as shown. Suppose that AP = 3, PQ = 9, and QC = 16. Then the area of ABCD can be expressed in the form m\\sqrt n, where m and n are positive integers, and n is not divisible by the square of any prime. 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": 5, "problem_name": "2022 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/22_aime_I_p12", "prev": "/problem/22_aime_I_p10"}}