104

Part of 1968 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 104 All Soviet Union MO 1968 a tetrahedron and 4 spheres

Source:

Three spheres are constructed so that the edges

[AB], [BC], [AD]

of the tetrahedron

ABCD

are their respective diameters. Prove that the spheres cover all the tetrahedron.

spheretetrahedrongeometry3D geometry