Let ABCD be a parallelogram and let P be a point inside it such that ∠PDA=∠PBA. Let ω1 be the excircle of PAB opposite to the vertex A. Let ω2 be the incircle of the triangle PCD. Prove that one of the common tangents of ω1 and ω2 is parallel to AD.Ivan Frolov geometryTournament of TownsKvant