Ajima-Malfatti Points

The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's Tangent Triangle Problem coincide in a point $Y$ called the first Ajima-Malfatti point (Kimberling and MacDonald 1990, Kimberling 1994). Similarly, letting $A''$, $B''$, and $C''$ be the excenters of $ABC$, then the lines $A'A''$, $B'B''$, and $C'C''$ are coincident in another point called the second Ajima-Malfatti point. The points are sometimes simply called the Malfatti Points (Kimberling 1994).

References

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Kimberling, C. ``1st and 2nd Ajima-Malfatti Points.'' http://cedar.evansville.edu/~ck6/tcenters/recent/ajmalf.html.

Kimberling, C. and MacDonald, I. G. ``Problem E 3251 and Solution. '' Amer. Math. Monthly 97, 612-613, 1990.