2021 AIME I #13

October 26, 2022 mathproblemsolvingskills

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 $AB$ intersections $\omega$ at two points $P$ and $Q$ such that the measure of minor arc $\widehat{PQ}$ is $120^{\circ}$ . Find the distance between the centers of $\omega_1$ and $\omega_2$ .

Published by mathproblemsolvingskills

I coach students preparing for MathCounts and the AMCs, and I teach using curricula published by Art of Problem Solving. View all posts by mathproblemsolvingskills

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