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The center of the Spieker Circle. It is the Centroid of the Perimeter of the original Triangle. The third Brocard Point is Collinear with the Spieker center and the Isotomic Conjugate Point of its Incenter.
See also Brocard Points, Centroid (Triangle), Incenter, Isotomic Conjugate Point, Perimeter, Spieker Circle, Taylor Center
References
Casey, J. A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing
an Account of Its Most Recent Extensions, with Numerous Examples, 2nd ed., rev. enl. Dublin: Hodges, Figgis, & Co., p. 81, 1893.
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 226-229 and 249, 1929.
Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.