The inner Soddy center (or inner Soddy point) is the center of the inner Soddy circle. It is equivalent to the equal detour point X_175 and has equivalent triangle center functions α_175 | = | 1 + sec(1/2 A) cos(1/2 B) cos(1/2 C) α_175 | = | 1 + (b c)/(2(-a + b + c) R), where R is the circumradius of the reference triangle. It lies on the Soddy line.

inner Soddy circle | outer Soddy center | Soddy circles