There exists a triangulation point for which the triangles , , and have equal Brocard angles. This point is a triangle center known as the equiBrocard center and is Kimberling center .
It has a complicated triangle center function given by the unique positive real root of a tenthorder polynomial in , which is actually fifthorder 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).