There exists a triangulation point 
for which the triangles 
, 
, and 
have equal Brocard angles.
This point is a triangle center known as the equi-Brocard center and is Kimberling
center 
.
It has a complicated triangle center function given by the unique positive real root of a tenth-order polynomial 
in 
, which is actually fifth-order in 
. The polynomial can be found by computing the distances
from each of the vertices to the triangulation point
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
and using the equation
 |
(4)
|
where 
is the Brocard angle and 
is the triangle area
to obtain the three equations
 |
(5)
|
where 
is the area of the triangle with side lengths 
, 
, and 
(which can be computed using Heron's
formula).
