{"status": "success", "data": {"description_md": "Let $\\overline{AB}$ be a diameter of circle $\\omega$. Extend $\\overline{AB}$ through $A$ to $C$. Point $T$ lies on $\\omega$ so that line $CT$ is tangent to $\\omega$. Point $P$ is the foot of the perpendicular from $A$ to line $CT$. Suppose $AB = 18$, and let $m$ denote the maximum possible length of segment $BP$. Find $m^{2}$.\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 \\overline{AB} be a diameter of circle \\omega. Extend \\overline{AB} through A to C. Point T lies on \\omega so that line CT is tangent to \\omega. Point P is the foot of the perpendicular from A to line CT. Suppose AB = 18, and let m denote the maximum possible length of segment BP. Find m^{2}.

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": "2008 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_I_p15", "prev": "/problem/08_aime_I_p13"}}