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

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

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

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (11)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info