Intersection of circles

Geometry Level 4

Circles Γ1 \Gamma_1 and Γ2\Gamma_2 have centers XX and YY respectively. They intersect at points AA and BB, such that angle XAY XAY is obtuse. The line AXAX intersects Γ2 \Gamma_2 again at PP, and the line AYAY intersects Γ1\Gamma_1 again at QQ. Lines PQPQ and XY XY intersect at GG, such that Q Q lies on line segment GPGP. If GQ=255 GQ = 255, GP=266 GP = 266 and GX=190GX = 190, what is the length of XYXY?

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