How to solve this geometry problem?

Circle A has radius 3 and circle B has radius 2. Their centers are 13 units from one another. A common external tangent PQ is drawn such that P lies on circle A and Q lies on circle B. Circles A' and B' are constructed outside circles A and B such that circle A' is tangent to segment AB, segment PQ, and circle A, and circle B' is tangent to segment AB, segment PQ, and circle B. What is the distance between the centers of A' and B'?