In the plane of any triangle ABC, let G be the centroid, and let

La = the bisector of angle A,
Lb = the bisector of angle B,
Lc = the bisector of angle C;

Ga = reflection of line AG about La,
Gb = reflection of line BG about Lb,
Gc = reflection of line CG about Lc.

The three lines Ga, Gb, Gc meet in the symmedian point, labeled K in the sketch. It is also known as the Lemoine point. For a particularly good discussion, see

Ross Honsberger, Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Mathematical Association of America, Washington, D.C., 1995.

Emil Lemoine (1840-1912)
Triangle Centers
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