Two circles \omega_{A} and \omega_{B} have centers at points A and B respectively and intersect at points P and Q in such a way that A, B, P, and Q all lie on a common circle \omega. The tangent to \omega at P intersects \omega_{A} and \omega_{B} again at points X and Y respectively. Suppose A B=17 and X Y=20. Compute the sum of the radii of \omega_{A} and \omega_{B}.