MathDB

3

Part of 1972 Dutch Mathematical Olympiad

Problems(1)

compare volumes , regular tetrahedra

Source: Netherlands - Dutch NMO 1972 p3

1/27/2023
ABCDABCD is a regular tetrahedron. The points P,Q,RP,Q,R and SS lie outside this tetrahedron in such a way that ABCPABCP, ABDQABDQ, ACDRACDR and BCDSBCDS are regular tetrahedra. Prove that the volume of the tetrahedron PQRSPQRS is less than the sum of the volumes of ABCPABCP,ABDQABDQ,ACDRACDR, BCDSBCDS and ABCDABCD.
geometrytetrahedrongeometric inequality3D geometry