There exists a triangulation point Y for which the triangles B Y C, C Y A, and A Y B have equal Brocard angles. This point is a triangle center known as the equi-Brocard center and is Kimberling center X_368. It has a complicated triangle center function given by the unique positive real root of a tenth-order polynomial f(a, b, c) in α, which is actually fifth-order in α^2.

Brocard angle | first Brocard point

Pierre René Jean Baptiste Henri Brocard