The Lester circle is the circle on which the circumcenter C, nine-point center N, and the first and second Fermat points X and X' lie. Besides these (Kimberling centers X_3, X_5, X_13, and X_14, respective), no other notable triangle centers lie on the circle. The Lester circle has circle function l = - (f(a, b, c) R^2[1 + 2cos(2A)])/(6a^2 b c(a^2 - b^2)(a^2 - c^2)), where f(a, b, c) = a^6 - 3a^4 b^2 + 3a^2 b^4 - b^6 - 3a^4 c^2 - a^2 b^2 c^2 + b^4 c^2 + 3a^2 c^4 + b^2 c^4 - c^6 does not appear to have a simple form and l does not appear in Kimberling's list of triangle centers.
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