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right tetrahedron at A

Source: 31-th Vietnamese Mathematical Olympiad 1993

February 17, 2007
geometry3D geometrytetrahedronspheregeometry proposed

Problem Statement

The tetrahedron ABCDABCD has its vertices on the fixed sphere SS. Prove that AB2+AC2+AD2−BC2−BD2−CD2AB^{2}+AC^{2}+AD^{2}-BC^{2}-BD^{2}-CD^{2} is minimum iff AB⊥AC,AC⊥AD,AD⊥ABAB\perp AC,AC\perp AD,AD\perp AB.
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