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prove that there exists an equilateral triangle ABC iff

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September 24, 2010
geometryTriangletriangle inequalityIMO Shortlist

Problem Statement

Given a point OO and lengths x,y,zx, y, z, prove that there exists an equilateral triangle ABCABC for which OA=x,OB=y,OC=zOA = x, OB = y, OC = z, if and only if x+y≥z,y+z≥x,z+x≥yx+y \geq z, y+z \geq x, z+x \geq y (the points O,A,B,CO,A,B,C are coplanar).
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