{"status": "success", "data": {"description_md": "Twelve congruent disks are placed on a circle $C$ of radius 1 in such a way that the twelve disks cover $C$, no two of the disks overlap, and so that each of the twelve disks is tangent to its two neighbors. The resulting arrangement of disks is shown in the figure below. The sum of the areas of the twelve disks can be written in the from $\\pi(a-b\\sqrt{c})$, where $a,b,c$ are positive integers and $c$ is not divisible by the square of any prime. Find $a+b+c$.

$\\includegraphics[width=126, height=126, totalheight=126]{https://latex.artofproblemsolving.com/a/c/2/ac2021daf5eeece87535256bce323198a5eda8e9.png}$\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": "

Twelve congruent disks are placed on a circle C of radius 1 in such a way that the twelve disks cover C, no two of the disks overlap, and so that each of the twelve disks is tangent to its two neighbors. The resulting arrangement of disks is shown in the figure below. The sum of the areas of the twelve disks can be written in the from \\pi(a-b\\sqrt{c}), where a,b,c are positive integers and c is not divisible by the square of any prime. Find a+b+c.

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": "1991 AIME Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/91_aime_p12", "prev": "/problem/91_aime_p10"}}