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Perpendicular lines with circumcenters

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September 1, 2010
geometrycircumcirclerhombusconvex quadrilateralIMO ShortlistIMO Longlist

Problem Statement

Let ABCDABCD be a convex quadrilateral such that AC=BDAC = BD. Equilateral triangles are constructed on the sides of the quadrilateral. Let O1,O2,O3,O4O_1,O_2,O_3,O_4 be the centers of the triangles constructed on AB,BC,CD,DAAB,BC,CD,DA respectively. Show that O1O3O_1O_3 is perpendicular to O2O4.O_2O_4.
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