{"status": "success", "data": {"description_md": "A circle with diameter $\\overline{PQ}$ of length 10 is internally tangent at $P$ to a circle of radius 20. Square $ABCD$ is constructed with $A$ and $B$ on the larger circle, $\\overline{CD}$ tangent at $Q$ to the smaller circle, and the smaller circle outside $ABCD$. The length of $\\overline{AB}$ can be written in the form $m + \\sqrt{n}$, where $m$ and $n$ are 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": "

A circle with diameter \\overline{PQ} of length 10 is internally tangent at P to a circle of radius 20. Square ABCD is constructed with A and B on the larger circle, \\overline{CD} tangent at Q to the smaller circle, and the smaller circle outside ABCD. The length of \\overline{AB} can be written in the form m + \\sqrt{n}, where m and n are 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": 3, "problem_name": "1994 AIME Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/94_aime_p03", "prev": "/problem/94_aime_p01"}}