Christopher J. Bradley and Geoff C. Smith, The locations of the Brocard points,
Forum Geometricorum, 6 (2006) 71--77.

Abstract:  We fix and scale to constant size the orthocentroidal disk of a variable non-equilateral triangle ABC. We show that the set of points of the plane which can be either type of Brocard point consists of the interior of the orthocentroidal disk. We give the locus of points which can arise as a Brocard point of specified type, and describe this region and its boundary in polar terms. We show that ABC is determined by the locations of the circumcenter, the centroid and the Brocard points. In some circumstances the location of one Brocard point will suffice.

[ps file] [pdf file]