The triangulation point 
of a reference triangle 
for which triangles 
, 
, and 
have congruent incircles.
It is a special case of an Elkies point. Kimberling
and Elkies (1987) showed that a unique such point exists for any triangle, but did
not provide explicit constructions for this point.
Congruent Incircles Point
See also
Congruent Incircles, Elkies Point, IncircleExplore with Wolfram|Alpha
References
Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. and Elkies, N. "Problem 1238 and Solution: A Congruent Incircle Point." Math. Mag. 60, 116-117, 1987.Referenced on Wolfram|Alpha
Congruent Incircles PointCite this as:
Weisstein, Eric W. "Congruent Incircles Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CongruentIncirclesPoint.html