The third Lemoine circle, a term coined here for the first time, is the circumcircle of the Lemoine triangle.
It has center function
(1)
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where is a 10th-order polynomial, which is not a Kimberling center and radius
(2)
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where
(3)
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Its circle function is
(4)
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which is also not a Kimberling center.
It passes through , the center of the Kiepert hyperbola.