{"status": "success", "data": {"description_md": "Circles $\\omega_1$ and $\\omega_2$ with radii $961$ and $625$, respectively, intersect at distinct points $A$ and $B$. A third circle $\\omega$ is externally tangent to both $\\omega_1$ and $\\omega_2$. Suppose line $AB$ intersects $\\omega$ at two points $P$ and $Q$ such that the measure of minor arc ${PQ}$ is $120^{\\circ}$. Find the distance between the centers of $\\omega_1$ and $\\omega_2$.\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": "

Circles \\omega_1 and \\omega_2 with radii 961 and 625, respectively, intersect at distinct points A and B. A third circle \\omega is externally tangent to both \\omega_1 and \\omega_2. Suppose line AB intersects \\omega at two points P and Q such that the measure of minor arc {PQ} is 120^{\\circ}. Find the distance between the centers of \\omega_1 and \\omega_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": "2021 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_I_p14", "prev": "/problem/21_aime_I_p12"}}