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If the Vertex 
of a Triangle describes the Neuberg Circle 
, its Median Point describes a circle whose radius is 1/3 that of the Neuberg Circle. Such a Circle is known as a McKay circle, and the three McCay circles are Concurrent at the
Median Point 
. Three homologous collinear points lie on the McCay circles.
See also Circle, Concurrent, Median Point, Neuberg Circles
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA:
Houghton Mifflin, pp. 290 and 306, 1929.