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The First Lemoine Circle

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Let ABC be a triangle and P be a point. The reflections of the three lines AP, BP, and CP in the angle bisectors at A, B, and C meet in a point, called the isogonal conjugate of P.

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The symmedian point is the isogonal conjugate of a triangle's centroid.

Through the symmedian point of a triangle ABC draw lines parallel to the triangle's sides. The six points of intersection of those lines with the triangle's sides are concyclic. The circle through those points is called the first Lemoine circle.

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Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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