Cosymmedian Triangles

Extend the Symmedian Lines of a Triangle $\Delta A_1A_2A_3$ to meet the Circumcircle at $P_1$, $P_2$, $P_3$. Then the Lemoine Point $K$ of $\Delta A_1A_2A_3$ is also the Lemoine Point of $\Delta P_1P_2P_3$. The Triangles $\Delta A_1A_2A_3$ and $\Delta P_1P_2P_3$ are cosymmedian triangles, and have the same Brocard Circle, second Brocard Triangle, Brocard Angle, Brocard Points, and Circumcircle.

See also Brocard Angle, Brocard Circle, Brocard Points, Brocard Triangles, Circumcircle, Lemoine Point, Symmedian Line