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 \(\omega_2\).
+1694 The distance between ω1 and ω2 seems to be identical to the length of a radius of a circle ω2.
The ratio of ab:bc must be 1:3 (The length of ac is irrelevant)
