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Serbia National Olympiad Day 1 Problem 1

Source: Serbia National Olympiad Day 1 Problem 1

March 28, 2015
geometrygeometry unsolvedcyclic quadrilateral

Problem Statement

Consider circle inscribed quadriateral ABCDABCD. Let M,N,P,QM,N,P,Q be midpoints of sides DA,AB,BC,CDDA,AB,BC,CD.Let EE be the point of intersection of diagonals. Let k1,k2k1,k2 be circles around EMNEMN and EPQEPQ . Let FF be point of intersection of k1k1 and k2k2 different from EE. Prove that EFEF is perpendicular to ACAC.
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