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China TST 1986 tetrahedron perimeter max inequality

Source: China TST 1986, problem 6

May 16, 2005
geometry3D geometrytetrahedronperimeterinequalitiesfunctiongeometry unsolved

Problem Statement

Given a tetrahedron ABCDABCD, EE, FF, GG, are on the respectively on the segments ABAB, ACAC and ADAD. Prove that: i) area EFG≤EFG \leq max{area ABCABC,area ABDABD,area ACDACD,area BCDBCD}. ii) The same as above replacing "area" for "perimeter".
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