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Source: IOM 2021 #6

December 10, 2021
geometry3D geometry

Problem Statement

Let ABCDABCD be a tetrahedron and suppose that MM is a point inside it such that ∠MAD=∠MBC\angle MAD=\angle MBC and ∠MDB=∠MCA\angle MDB=\angle MCA. Prove that MA⋅MB+MC⋅MD<max⁡(AD⋅BC,AC⋅BD).MA\cdot MB+MC\cdot MD<\max(AD\cdot BC,AC\cdot BD).
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