Egan conjecture

Conjecture in geometry

In geometry, the Egan conjecture gives a sufficient and necessary condition for the radii of two spheres and the distance of their centers, so that a simplex exists, which is completely contained inside the larger sphere and completely encloses the smaller sphere. The conjecture generalizes an equality discovered by William Chapple, which is a special case of Poncelet's closure theorem, as well as the Grace–Danielsson inequality in one dimension higher.

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