The Lemoine axis is the perspectrix of a reference triangle and its tangential triangle, and also the trilinear polar of the symmedian point K of the reference triangle. It is also the polar of K with regard to the circumcircle, and is perpendicular to the Brocard axis. The centers of the Apollonius circles are collinear on the Lemoine axis. This line is perpendicular to the Brocard axis O K and is the radical line of the circumcircle and the Brocard circle.

Apollonius circle | Brocard axis | circumcircle | collinear | first Lemoine circle | polar | radical line | symmedian | symmedian point | tangential triangle | triangle centroid | trilinear polar