The diagonals of convex quadrilateral $ABCD$ are perpendicular. Points $A' , B' , C' , D' $ are the circumcenters of triangles $ABD, BCA, CDB, DAC$ respectively. Prove that lines $AA' , BB' , CC' , DD' $ concur. (A. Zaslavsky)
Problem
Source: Sharygin Geometry Olympiad 2015 Final 9.6
Tags: geometry, concurrency, concurrent, diagonals