{"status": "success", "data": {"description_md": "Three concentric circles have radii $3$, $4$, and $5$. An equilateral triangle with one vertex on each circle has side length $s$. The largest possible area of the triangle can be written as $a+\\frac{b}{c}\\sqrt{d}$, where $a,b,c$ and $d$ are positive integers, $b$ and $c$ are relatively prime, and $d$ 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": "

Three concentric circles have radii 3, 4, and 5. An equilateral triangle with one vertex on each circle has side length s. The largest possible area of the triangle can be written as a+\\frac{b}{c}\\sqrt{d}, where a,b,c and d are positive integers, b and c are relatively prime, and d 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": 6, "problem_name": "2012 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_I_p14", "prev": "/problem/12_aime_I_p12"}}