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Convex quad

Source: USAMO 1993

October 27, 2005
geometryUSAMO

Problem Statement

Let  ABCD \, ABCD \, be a convex quadrilateral such that diagonals  AC \, AC \, and  BD \, BD \, intersect at right angles, and let  E \, E \, be their intersection. Prove that the reflections of  E \, E \, across  AB, BC, CD, DA \, AB, \, BC, \, CD, \, DA \, are concyclic.
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