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I have question regarding the possibility of inscribing a cone in a sphere.

Essentially, I am looking for some proper definition of that. When dealing with polyhedra, the matter is simple: each of the polyhedron's vertices must lie on the sphere. However, what conditions need to be met in order for a cone to be inscribed in a sphere? When the base is circular, I understand that the apex of the cone and the edge of the base must lie on the sphere. But can an elliptical cone be inscribed in a sphere, and if yes, would that mean that just two points from the edge of the base are on that sphere?

Intuition seems to say "yes", but as I mentioned, I would be thankful for some definition.

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    Yes, Theophile, a problem was asking for the largest cone inscribed in a sphere. The problem itself is quite easy, and yes, the largest cone is indeed in this case a right circular - for obvious reasons. However, as I was ruling out the other options in the beginning (for example, a cone with the axis not perpendicular to the base), I was wondering if a cone with an elliptical base _was_ _even_ _an_ _option_. If yes, the explanation is obviously simple (the area of the base can be expanded to a circle).2012-09-04

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