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angle chasing with an orthodiagonal ABCD

Source: Indonesia MO (INAMO) 2016 P1

September 14, 2018
geometryperpendicularangle bisectorprojections

Problem Statement

Let ABCDABCD be a cyclic quadrilateral wih both diagonals perpendicular to each other and intersecting at point OO. Let E,F,G,HE,F,G,H be the orthogonal projections of OO on sides AB,BC,CD,DAAB,BC,CD,DA respectively. a. Prove that ∠EFG+∠GHE=180o\angle EFG + \angle GHE = 180^o b. Prove that OEOE bisects angle ∠FEH\angle FEH .
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