The line segment 
joining the symmedian point 
and circumcenter 
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
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is the first Brocard point, 
is the circumradius, and
is the Brocard
angle. Its midpoint is the center of the Brocard
circle, which has equivalent triangle
center functions
 |  |  |
(4)
|
 |  |  |
(5)
|
where 
is the Brocard angle, and is Kimberling
center 
(Kimberling 1998, p. 102), which is also the center of the first
Lemoine circle.
