Find the side length of the smallest equilateral triangle in which three discs of radii of 2, 3, 4 can be placed without overlap.
The length L, I believe, is L = 11 sqrt(3)
The method is this:
Wedge the 4 radius circle into one corner of a large triangle, and the
3 radius into another corner, then shorten the length until they touch.
It turns out the 2 radius circle will then fit easily and is not a constraint. I believe (with no proof) this is the minimum arrangement. A figure with the work is
here.
Edited on December 13, 2018, 12:28 pm
soln
