The three circumcircles through the triangle centroid 
of a given triangle 
and the pairs of the vertices of the second
Brocard triangle are called the McCay circles (Johnson 1929, p. 306).
The circumcircle of their centers (i.e., of the second Brocard triangle) is therefore the Brocard circle.
The 
-McCay circle has center function
 |
and radius,
 |
1/3 that of the Neuberg circle, where 
is the Brocard angle
(Johnson 1929, p. 307).
If the polygon vertex 
of a triangle describes a Neuberg circle 
, then its triangle centroid 
describes one of the McCay circles (Johnson
1929, p. 290). In the above figure, the inner triangle is the second Brocard
triangle of 
,
whose two indicated edges are concyclic with 
on the McCay circle.
