2021 AIME I Problem 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.

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.