MathDB

3

Part of 1989 ITAMO

Problems(1)

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

Source: 1989 ITAMO p3

1/31/2020
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.
tetrahedron3D geometrygeometryVolume