Question

Circles Γ1 and Γ2 have centers X and Y respectively. They intersect at points A and B, such that angle XAY is obtuse. The line AX intersects Γ2 again at P, and the line AY intersects Γ1 again at Q. Lines PQ and XY intersect at G, such that Q lies on line segment GP. If GQ=255, GP=266 and GX=190, what is the length of XY?