The Brocard Points and Neuberg Circles of a Triangle
In the triangle shown, the Brocard point (red) is the only point such that the alternating gray-blue angles are all equal. The measure of this angle is called the Brocard angle.
The second Brocard point is similarly defined using the other adjacencies with the sides.
A Neuberg circle is the locus of points through which one vertex can vary (keeping the other two fixed) while preserving the Brocard angle. You can drag the vertices to change the triangle or drag them around the Neuberg circles when the circles are shown.