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?
Looking at Charlie's last post, I notice that some values of (a, b, c) give a maximum angle of 180 degrees:
(1, 4, 4) and (1, 2.25, 9)
I wonder what other values result in a 180 degree angle?
Looking back at Charlie's first post, and Steve Herman's formula, and setting a=1:
When 1=(bc)/(b+c+2sqrt(bc)) then the angle will be 180 degrees.
This corresponds to the smalled sphere just fitting directly beneath the larger 2 tangent spheres.
Edited on September 17, 2005, 2:47 pm
Posted by Larry
on 2005-09-17 14:32:32