Spieker radical circle

The radical circle of the excircles has center at the Spieker center X_10 and radius R_E = 1/2 sqrt((a^2 b + a b^2 + a^2 c + a b c + b^2 c + a c^2 + b c^2)/(a + b + c)). Its circle function is l = (a^3 - a b^2 + 2a b c - a c^2)/(4a b c), corresponding to X_56, the external similitude center of the incircle and circumcircle. No Kimberling centers lie on it.

central circle | excircles | radical circle