{"status": "success", "data": {"description_md": "Given a circle of radius $\\sqrt{13}$, let $A$ be a point at a distance $4 + \\sqrt{13}$ from the center $O$ of the circle. Let $B$ be the point on the circle nearest to point $A$. A line passing through the point $A$ intersects the circle at points $K$ and $L$. The maximum possible area for $\\triangle BKL$ can be written in the form $\\tfrac{a-b\\sqrt{c}}{d}$, where $a$, $b$, $c$, and $d$ are positive integers, $a$ and $d$ are relatively prime, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\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": "

Given a circle of radius \\sqrt{13}, let A be a point at a distance 4 + \\sqrt{13} from the center O of the circle. Let B be the point on the circle nearest to point A. A line passing through the point A intersects the circle at points K and L. The maximum possible area for \\triangle BKL can be written in the form \\tfrac{a-b\\sqrt{c}}{d}, where a, b, c, and d are positive integers, a and d are relatively prime, and c is not divisible by the square of any prime. Find a+b+c+d.

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": "2013 AIME II Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_II_p11", "prev": "/problem/13_aime_II_p09"}}