Intersection of circles

Geometry Level pending

Circles \( \Gamma_1 \) and \(\Gamma_2\) have centers \(X\) and \(Y\) respectively. They intersect at points \(A\) and \(B\), such that angle \( XAY\) is obtuse. The line \(AX\) intersects \( \Gamma_2\) again at \(P\), and the line \(AY\) intersects \(\Gamma_1\) 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 \(XY\)?

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