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?

(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