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prove concyclicity of projections in quadrilateral if diagonals orthogonal

Source: Moldova 2000 Grade 9 P3

April 25, 2021
geometry

Problem Statement

The diagonals of a convex quadrilateral ABCDABCD are orthogonal and intersect at a point EE. Prove that the projections of EE on AB,BC,CD,DAAB,BC,CD,DA are concyclic.