The symmedial circle is the circumcircle of the symmedial triangle. It has circle function l = (b c(a^4 - a^2 b^2 - b^4 - a^2 c^2 - b^2 c^2 - c^4))/(2(a^2 + b^2)(a^2 + c^2)(b^2 + c^2)), which does not correspond to any Kimberling center, and radius R_S = sqrt(f(a, b, c) f(b, c, a) f(c, a, b))/(2(a^2 + b^2)(b^2 + c^2)(c^2 + a^2)) R, where R is the circumradius of the reference triangle and f(a, b, c) = a^4 - 3b^2 a^2 - c^2 a^2 + b^4 - c^4 - b^2 c^2.
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