Egan conjecture
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 (and later independently by Leonhard Euler), which is a special case of Poncelet's closure theorem, as well as the Grace–Danielsson inequality in one dimension higher.