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    First Neuberg Circle

    Definition

    The first Neuberg circle is the circumcircle of the first Neuberg triangle. The center has center function α = (-c^2 b^6 + a^4 b^4 + a^2 c^2 b^4 - c^6 b^2 + a^2 c^4 b^2 + a^4 c^2 b^2 + a^4 c^4)/a, which is not a Kimberling center. Its radius is R_N = sqrt(f(a, b, c) f(b, c, a) f(c, a, b))/(16Δ^2(a^2 b^2 + c^2 b^2 + a^2 c^2)), where f(a, b, c) = a^6 + b^2 a^4 + b^4 a^2 - b^2 c^2 a^2 + b^6 and Δ is the area of the reference triangle.

    Associated person

    Joseph Jean Baptiste Neuberg

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