"Three circles packed inside a triangle such that each is tangent to the other two and to two sides of the triangle are known as Malfatti circles" (for a brief historical account on this topic, see [here](http://mathworld.wolfram.com/MalfattiCircles.html) and [here](http://mathworld.wolfram.com/MalfattisProblem.html) on MathWorld).


Consider the triangle formed by the centers of these circles, one can draw a new set of smaller Malfatti circles in this triangle. What is the limiting point of this process?


One thing sort of discouraging is that I tried on an isosceles triangle, unfortunately did not find the limiting point matching any of the known relevant points (e.g., incenter or [the first Ajima-Malfatti point](http://mathworld.wolfram.com/Ajima-MalfattiPoints.html)).



Malfatti Circles - Limiting point
I don't know the answer to your question, but it should be easy enough to compute this limit point numerically for an arbitrary triangle and use the result to [search the Encyclopedia of Triangle Centers](http://faculty.evansville.edu/ck6/encyclopedia/search.html).


