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Friday, September 17, 2010
14th Balkan Mathematical Olympiad Problems 1997
14th Balkan Mathematical Olympiad Problems 1997A1. ABCD is a convex quadrilateral. X is a point inside it. XA2 + XB2 + XC2 + XD2 is twice the area of the quadrilateral. Show that it is a square and that X is its center.
