TITLE: Malfatti Circles - Limiting point
QUESTION [5 upvotes]: "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 and here 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).

REPLY [5 votes]: 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.