What is the name of the circle that is tangent to three mutually-tangent circles centered at the vertices of a triangle?

Question

I want some information about the little 'tangent circle', but I don't have its name to search for it in the internet. What is it called?

Answer 1

I think that's the Inner Soddy Circle.

Answer 2

I think that (inner) Soddy circle is what you want.