The inner Soddy center (or inner Soddy point) is the center of the inner Soddy circle. It is equivalent to the equal detour point (Kimberling 1994) and has equivalent triangle center functions
where is the circumradius of the reference triangle.
It lies on the Soddy line.
More things to try:
Weisstein, Eric W. "Inner Soddy Center." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InnerSoddyCenter.html
(Kimberling 1994) and has equivalent triangle center functions
is the circumradius of the reference
triangle.
