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 Tetrahedron bounded by spheres (Posted on 2003-04-17)
A regular tetrahedron holds a sphere snugly within its four sides. A larger sphere surrounds the tetrahedron, just touching its four vertices. What is the ratio of radii of the two spheres?

 See The Solution Submitted by Bryan Rating: 3.5000 (6 votes)

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 re: Solution (long and complicated version) | Comment 5 of 7 |
(In reply to Solution (long and complicated version) by Hank)

Regarding "knowing that all of the angles in the tetrahedron are 60*, half would be 30*. ", those are only the angles on a face that are 60°. C, the center of the tetrahedron, is not on a face. One of the angles in the rt triangle through the center is the dihedral angle between two faces of the tetrahedron and is arccos(1/3) = 70.528779... degrees.
 Posted by Charlie on 2003-04-17 10:04:54

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