The Mandart circle is the circumcircle of the extouch triangle. It has center at Kimberling center X_1158, which has trilinear center function α_1158 = a^6 - 3a^4 b^2 + 3a^2 b^4 - b^6 + 2a^4 b c + 2a^3 b^2 c - 2a^2 b^3 c - 2a b^4 c - 3a^4 c^2 + 2a^3 b c^2 - 2a^2 b^2 c^2 + 2a b^3 c^2 + b^4 c^2 - 2a^2 b c^3 + 2a b^2 c^3 + 3a^2 c^4 - 2a b c^4 + b^2 c^4 - c^6, and radius R_M = s/(a b c) sqrt((4R^2 - b c)(4R^2 - c a)(4R^2 - a b)), where R is the circumradius of the reference triangle and s is the semiperimeter. It has trilinear circle function l = - (a^3 + a^2 b - a b^2 - b^3 + a^2 c - 2a b c + b^2 c - a c^2 + b c^2 - c^3)/(4b(a - b - c) c), which corresponds to Kimberling center X_221.

central circle | extouch triangle