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Geometry, Serbia MO 2017

Source: Serbia MO 2017 P2

April 1, 2017
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a convex and cyclic quadrilateral. Let AD∩BC={E}AD\cap BC=\{E\}, and let M,NM,N be points on AD,BCAD,BC such that AM:MD=BN:NCAM:MD=BN:NC. Circle around △EMN\triangle EMN intersects circle around ABCDABCD at X,YX,Y prove that AB,CDAB,CD and XYXY are either parallel or concurrent.
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