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MN x NP x PQ x QM >= AM x BN x CP xDQ , regular tetrahedron

Source: 1999 Romania NMO X p2

August 14, 2024
geometry3D geometrytetrahedrongeometric inequalityGeometric Inequalities

Problem Statement

On the sides (AB)(AB), (BC)(BC), (CD)(CD) and (DA)(DA) of the regular tetrahedron ABCDABCD, one considers the points MM, NN, PP, QQ, respectively Prove that MN⋅NP⋅PQ⋅QM≥AM⋅BN⋅CP⋅DQ.MN \cdot NP \cdot PQ \cdot QM \ge AM \cdot BN \cdot CP \cdot DQ.
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