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compare volumes , regular tetrahedra

Source: Netherlands - Dutch NMO 1972 p3

January 27, 2023
geometrytetrahedrongeometric inequality3D geometry

Problem Statement

ABCDABCD is a regular tetrahedron. The points P,Q,RP,Q,R and SS lie outside this tetrahedron in such a way that ABCPABCP, ABDQABDQ, ACDRACDR and BCDSBCDS are regular tetrahedra. Prove that the volume of the tetrahedron PQRSPQRS is less than the sum of the volumes of ABCPABCP,ABDQABDQ,ACDRACDR, BCDSBCDS and ABCDABCD.
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