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Bosnia and Herzegovina JBMO TST 2016 Problem 3

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2016

September 16, 2018
geometryperpendicularquadrilateralperimeter

Problem Statement

Let OO be a center of circle which passes through vertices of quadrilateral ABCDABCD, which has perpendicular diagonals. Prove that sum of distances of point OO to sides of quadrilateral ABCDABCD is equal to half of perimeter of ABCDABCD.
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