Mathematics · Geometry

Let C1 and C2 be two circles which do not touch or intersect each other, and let O1 and O2 be the centers of the circles, respectively. Let AB be the common transverse tangent to the circles such that P and Q are the points of tangency to C1 and C2 respectively. Let R be the point of intersection of O1O2 and AB. If ∠PO1R = 60°, find ∠QO2R and ∠QRO2, respectively.