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ABCD is cyclic and has area equal to 8

Source: Romanian JBMO TST 2006, Day 3, Problem 1

May 16, 2006
geometrycyclic quadrilateralgeometry unsolved

Problem Statement

Let ABCDABCD be a cyclic quadrilateral of area 8. If there exists a point OO in the plane of the quadrilateral such that OA+OB+OC+OD=8OA+OB+OC+OD = 8, prove that ABCDABCD is an isosceles trapezoid.
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