IMO Shortlist 2008 problem G3


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2. travnja 2012.
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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 \angle PAE = \angle QDE and \angle PBE = \angle QCE. Show that the quadrilateral ABCD is cyclic.

Proposed by John Cuya, Peru
Izvor: Međunarodna matematička olimpijada, shortlist 2008