Let ABCD be a cyclic quadrilateral with circumcircle Ω and let diagonals AC and BD intersect at X. Suppose that AEFB is inscribed in a circumcircle of triangle ABX such that EF and AB are parallel. FX meets the circumcircle of triangle CDX again at G. Let EX meets AB at P, and XG meets CD at Q. Denote by S the intersection of the perpendicular bisector of EG and Ω such that S is closer to A than B. Prove that line through S parallel to PQ is tangent to Ω. geometrycyclic quadrilateralcircumcircleperpendicular bisectortangent