Question 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 $AB$ intersects $\omega$ 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 $\omega_2.$