The radical circle of the Neuberg circles has circle function l = (a^2 b^4 - b^4 c^2 + a^2 c^4 - b^2 c^4)/(b c(a^2 b^2 + a^2 c^2 + b^2 c^2)), which does not correspond to any Kimberling center.

Neuberg circles | radical circle

Joseph Jean Baptiste Neuberg