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Six spheres

Source:

September 14, 2010
geometry3D geometryspheretetrahedrongeometry unsolved

Problem Statement

a) The solid SS is defined as the intersection of the six spheres with the six edges of a regular tetrahedron TT, with edge length 11, as diameters. Prove that SS contains two points at a distance 16.\frac{1}{\sqrt 6}.
b) Using the same assumptions in a), prove that no pair of points in SS has a distance larger than 16.\frac{1}{\sqrt 6}.
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