Brocard Diameter

The Line Segment $\overline{KO}$ joining the Lemoine Point $K$ and Circumcenter $O$ of a given Triangle. It is the Diameter of the Triangle's Brocard Circle, and lies along the Brocard Axis. The Brocard diameter has length

$$\overline{OK}={\overline{O\Omega}\over\cos\omega}={R\sqrt{1-4\sin^2\omega}\over\cos\omega},$$

where $\Omega$ is the first Brocard Point, $R$ is the Circumradius, and $\omega$ is the Brocard Angle.

See also Brocard Axis, Brocard Circle, Brocard Line, Brocard Points