The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated 6th-order polynomial. Its center lies on the lines (5, 19), (26, 55), and (30, 40), and is therefore is on a line parallel to the Euler line through X_40. Its radius however is given by the nice expression R_E = (a^2 b^2 c^2[S^2 + a b c(a + b + c)])/(4(a + b + c) S S_A S_B S_C), where S, S_A, S_B, and S_C are Conway triangle notation. No Kimberling centers lie on the extangents circle.
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