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tetrahedra PABC,PABD,PACD,PBCD have equal volumes, P interior of tetr.ABCD

Source: 1989 ITAMO p3

January 31, 2020
tetrahedron3D geometrygeometryVolume

Problem Statement

Prove that, for every tetrahedron ABCDABCD, there exists a unique point PP in the interior of the tetrahedron such that the tetrahedra PABC,PABD,PACD,PBCDPABC,PABD,PACD,PBCD have equal volumes.
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