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in a convex ABCD with perpendicular diagonals, 4 lines are concurrent

Source: Sharygin Geometry Olympiad 2015 Final 9.6

August 1, 2018
geometryconcurrencyconcurrentdiagonals

Problem Statement

The diagonals of convex quadrilateral ABCDABCD are perpendicular. Points A′,B′,C′,D′A' , B' , C' , D' are the circumcenters of triangles ABD,BCA,CDB,DACABD, BCA, CDB, DAC respectively. Prove that lines AA′,BB′,CC′,DD′AA' , BB' , CC' , DD' concur.
(A. Zaslavsky)
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