The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle Δ S_A S_B S_C. Its center has center function α = - ((b^2 - c^2) f(a, b, c))/a, where f(a, b, c) = a^8 - 4b^2 a^6 - 4c^2 a^6 + 6b^4 a^4 + 6c^4 a^4 + b^2 c^2 a^4 - 4b^6 a^2 - 4c^6 a^2 + b^2 c^4 a^2 + b^4 c^2 a^2 + b^8 + c^8 - 2b^2 c^6 + 2b^4 c^4 - 2b^6 c^2, which is not a Kimberling center.

Steiner circle | Steiner triangle