tetrahedron inscribed in a cube of side-length 1
Source: Romanian Nationals RMO 2005 - grade 8, problem 1
March 31, 2005
geometry3D geometrytetrahedronanalytic geometrytrigonometry
Problem Statement
We consider a cube with sides of length 1. Prove that a tetrahedron with vertices in the set of the vertices of the cube has the volume if and only if 3 of the vertices of the tetrahedron are vertices on the same face of the cube.
Dinu Serbanescu