Three spheres of radii a, b, and c are tangent to the same plane at points A, B, and C respectively. Each sphere is externally tangent to the other two.
If a < b < c, then which internal angle of triangle ABC is largest and what is its value in terms of a, b, and c?

IF there is an unique answer, then it should work for, say, a very small a and very large, almost equal, b and c. And in that case, A would almost lie on BC, so its angle would be the largest.

Posted by Federico Kereki on 2005-09-15 02:39:15