The midpoint of the first and second Brocard
points 
and 
.
It has equivalent triangle center functions
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the Brocard angle. It is Kimberling
center 
(Kimberling 1998, p. 73).
The Brocard midpoint lies on the Brocard axis and is the center of the Gallatly, half-Moses, and Moses circles.
