IMO 1985 LL NET57
The solid S is defined as the intersection of the six spheres with
IMO 1985 LL NET57
Origin: NET
Problem
The solid S is defined as the intersection of the six spheres with the six edges of a regular tetrahedron T , with edge length 1, as diameters. Prove that S contains two points at a distance \sqrt 6. (NET 1a) Using the same assumptions, prove that no pair of points in S has a distance larger than \sqrt 6.