MathDB
Centroids of tetrahedra, volume

Source: Austrian-Polish 1985, Problem 6

July 5, 2015
geometry3D geometrytetrahedronVolume

Problem Statement

Let PP be a point inside a tetrahedron ABCDABCD and let SA,SB,SC,SDS_A,S_B,S_C,S_D be the centroids (i.e. centers of gravity) of the tetrahedra PBCD,PCDA,PDAB,PABCPBCD,PCDA,PDAB,PABC. Show that the volume of the tetrahedron SASBSCSDS_AS_BS_CS_D equals 1/641/64 the volume of ABCDABCD.
Back to ProblemsView on AoPS