The above applet demonstrates the position of the brocard points relative to the disc on diameter GH (where G is the centroid and H the Orthocentre). In *The locations of the Brocard points* C.J.Bradley and G.C.Smith note that at least one of the pair will be found within the disc, unless both are on the boundary. You can test this by moving the points A,B and C: the positions of the Brocard points are also shown relative to the disc (in red) which can be repositioned for convenience.

Applet development in Cinderella