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R/r of set of tetrahedra with concentric inscribed + circumscribed spheres

Source: Austrian - Polish 1986

May 16, 2019
geometrytetrahedronsphereconcentricinscribedcircumscribed3D geometry

Problem Statement

Let MM be the set of all tetrahedra whose inscribed and circumscribed spheres are concentric. If the radii of these spheres are denoted by rr and RR respectively, find the possible values of R/rR/r over all tetrahedra from MM .
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