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equal sums of volumes of tetrahedra, pyramid with base #

Source: Russian Regional Olympiad 2010 11.6

August 24, 2024
geometry3D geometryVolumetetrahedron

Problem Statement

At the base of the quadrangular pyramid SABCDSABCD lies the parallelogram ABCDABCD. Prove that for any point OO inside the pyramid, the sum of the volumes of the tetrahedra OSABOSAB and OSCDOSCD is equal to the sum of the volumes of the tetrahedra OSBCOSBC and OSDAOSDA .
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