perplexus.info :: Geometry : Three Spheres

Three Spheres (Posted on 2005-09-14)

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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Puzzle Thoughts

Comment 6 of 6 |

The internal angle A is the largest, and:

arccos[(a*b-b*c+c*a)*sqrt(b*c)

A =---------------------------------------------------

2*a*b*c

Edited on August 6, 2023, 9:18 am

Posted by K Sengupta on 2023-08-06 09:17:17

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