I came across Malfatti's problem and just wondered what would happen if I inscribed three tangent circles in a square instead of a triangle. I read goldberg's 'on the original malfatti problem' Let me quote; A maximum area is not reached unless each circle is restrained from growing by making at least three contacts, either with the sides of the triangle or with other circles.
The problem I am trying to solve: Inscribe three tangent circles in a square. Are the maximum area also reached by the principles? (Refer it as problem A')
Look at circle G. Three constraints are on the same semicircle. Yet I think it is a possible maximum.
