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IMO Shortlist 2008, Geometry problem 3

Source: IMO Shortlist 2008, Geometry problem 3

July 9, 2009
geometrycircumcirclehomothetytrigonometryquadrilateralIMO ShortlistInversion

Problem Statement

Let ABCD ABCD be a convex quadrilateral and let P P and Q Q be points in ABCD ABCD such that PQDA PQDA and QPBC QPBC are cyclic quadrilaterals. Suppose that there exists a point E E on the line segment PQ PQ such that \angle PAE \equal{} \angle QDE and \angle PBE \equal{} \angle QCE. Show that the quadrilateral ABCD ABCD is cyclic. Proposed by John Cuya, Peru
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