Let ABCD be a cyclic quadrilateral inscribed in a circle ω with center O. The lines AD and BC meet at E, while the lines AB and CD meet at F. Let P be a point on the segment EF such that OP⊥EF. The circle Γ1 passes through A and E and is tangent to ω at A, while Γ2 passes through C and F and is tangent to ω at C. If Γ1 and Γ2 meet at X and Y, prove that PO is the bisector of ∠XPY.Proposed by Nikola Velov geometrycyclic quadrilateralcomplete quadrilateraltangent circlesangle bisector