The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_26, which has center function α_26 = a[-a^2 cos(2A) + b^2 cos(2B) + c^2 cos(2C)] (Kimberling 1994) and its radius is R_T = R/(4 left bracketing bar cos A cos B cos C right bracketing bar ), where R is the circumradius of the reference triangle. It has circle function l = (a^2 b c)/((a^2 + b^2 - c^2)(a^2 - b^2 + c^2)), corresponding to the circumcenter O of the reference triangle (X_3).

central circle | tangential triangle