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Cyclic quadrilateral

Source: Polish MO second round 2011

February 19, 2012
geometrygeometric transformationreflectiongeometry unsolved

Problem Statement

The convex quadrilateral ABCDABCD is given, AB<BCAB<BC and AD<CDAD<CD. P,QP,Q are points on BCBC and CDCD respectively such that PB=ABPB=AB and QD=ADQD=AD. MM is midpoint of PQPQ. We assume that ∠BMD=90∘\angle BMD=90^{\circ}, prove that ABCDABCD is cyclic.
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