Brocard Midpoint

The Midpoint of the Brocard Points. It has Triangle Center Function

$$\alpha=a(b^2+c^2)=\sin(A+\omega),$$

where $\omega$ is the Brocard Angle. It lies on the Brocard Axis.

References

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.