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Prove that there exist a triangle with sides x,y,z

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September 22, 2010
geometry3D geometrytetrahedronIMO Shortlist

Problem Statement

Given a tetrahedron ABCDABCD, let x=AB⋅CDx = AB \cdot CD, y=AC⋅BDy = AC \cdot BD, and z=AD⋅BCz = AD \cdot BC. Prove that there exists a triangle with edges x,y,z.x, y, z.
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