IMO 2008 Shortlist G3
Let ABCD be a convex quadrilateral and let P and Q be points in ABCD such that PQDA and QPBC are cyclic quadrilaterals. ...
Category: Geometry
Problem
Let ABCD be a convex quadrilateral and let P and Q be points in ABCD such that PQDA and QPBC are cyclic quadrilaterals. Suppose that there exists a point E on the line segment PQ such that ∠PAE = ∠QDE and ∠PBE = ∠QCE. Show that the quadrilateral ABCD is cyclic.