MathDB

11.6

Part of 2010 All-Russian Olympiad Regional Round

Problems(1)

equal sums of volumes of tetrahedra, pyramid with base #

Source: Russian Regional Olympiad 2010 11.6

8/24/2024
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 .
geometry3D geometryVolumetetrahedron