IMO 1973 SL 7

Given a tetrahedron ABCD, let x = AB \cdot CD, y = AC \cdot BD,

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IMO 1973 SL 7

Origin: POL

Problem

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

Solution

The result follows immediately from Ptolemy’s inequality.