{"status": "success", "data": {"description_md": "Circles $\\mathcal{C}_{1}$ and $\\mathcal{C}_{2}$ intersect at two points, one of which is $(9,6),$ and the product of the radii is $68.$ The x-axis and the line $y=mx$, where $m>0,$ are tangent to both circles. It is given that $m$ can be written in the form $a\\sqrt{b}/c,$ where $a,$ $b,$ and $c$ are positive integers, $b$ is not divisible by the square of any prime, and $a$ and $c$ are relatively prime. Find $a+b+c.$\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": "

Circles \\mathcal{C}_{1} and \\mathcal{C}_{2} intersect at two points, one of which is (9,6), and the product of the radii is 68. The x-axis and the line y=mx, where m>0, are tangent to both circles. It is given that m can be written in the form a\\sqrt{b}/c, where a, b, and c are positive integers, b is not divisible by the square of any prime, and a and c are relatively 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": 6, "problem_name": "2002 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/02_aime_II_p14"}}