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Show that O1O3 is perpendicular to O2O4

Source: Iran Third Round Problems 1993 – Poblem 5

July 29, 2011
geometry unsolvedgeometry

Problem Statement

In a convex quadrilateral ABCDABCD, diagonals ACAC and BDBD are equal. We construct four equilateral triangles with centers O1,O2,O3,O4O_1,O_2,O_3,O_4 on the sides sides AB,BC,CD,DAAB, BC, CD, DA outside of this quadrilateral, respectively. Show that O1O3⊥O2O4O_1O_3 \perp O_2O_4.
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