The McCay circles of a triangle 
are the three circumcircles
through its triangle centroid 
and pairs of vertices of
its second Brocard triangle (Johnson 1929,
p. 306).
The 
-McCay circle passes through 
, 
,
and 
, where 
, 
,
and 
are the vertices
of the second Brocard triangle. If 
is the center of the corresponding
Neuberg circle, then its center 
is given using vectors from a
common origin by
 |
Thus it is the image of 
under the homothecy taking 
to 
with scale factor 1/3 (Johnson 1929, p. 307). Its radius is
 |
1/3 that of the corresponding Neuberg circle, where 
and 
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 vertices are concyclic
with 
on the McCay circle.
