2021 AIME I #13

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.


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