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Three Spheres (Posted on 2005-09-14) Difficulty: 3 of 5
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?

See The Solution Submitted by Bractals    
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Some Thoughts No calculus answer, for the first part | Comment 2 of 5 |
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
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