MathDB

1

Part of 2015 Serbia National Math Olympiad

Problems(1)

Serbia National Olympiad Day 1 Problem 1

Source: Serbia National Olympiad Day 1 Problem 1

3/28/2015
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.
geometrygeometry unsolvedcyclic quadrilateral