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Tetrahedron inequality

Source: Izho 2017 P6

January 15, 2017
geometry3D geometrytetrahedroninequalities

Problem Statement

Let ABCDABCD be the regular tetrahedron, and M,NM, N points in space. Prove that: AM⋅AN+BM⋅BN+CM⋅CN≥DM⋅DNAM \cdot AN + BM \cdot BN + CM \cdot CN \geq DM \cdot DN
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