The circle passing through the isodynamic points 
and 
and the triangle
centroid 
of a triangle 
(Kimberling 1998, pp. 227-228).
The Parry circle has circle function
 |
(1)
|
which does not correspond to any noted triangle center. The center has triangle center function
 |
(2)
|
which is Kimberling center 
(Kimberling 1998, p. 232), and the radius is
 |  | ![(abc[(a^4+b^4+c^4)-(a^2b^2+b^2c^2+a^2c^2)])/(3|(a^2-b^2)(b^2-c^2)(c^2-a^2)|)](/images/equations/ParryCircle/Inline8.svg) |
(3)
|
 |  |  |
(4)
|
(P. Moses, pers. comm., Jan. 1, 2005), where 
, 
,
and 
is Conway
triangle notation.
The Parry circle and the circumcircle of a triangle intersect in two points: the focus of the Kiepert parabola and the so-called Parry point.
The Parry circle passes through Kimberling centers 
for 
(triangle centroid 
) 15, 16 (first and second isodynamic
points 
and 
), 23 (far-out
point), focus of the Kiepert parabola 110,
Parry point 111 (Kimberling 1998, p. 227), as
well as 352 and 353.
It is orthogonal to the Brocard circle, circumcircle, Lucas circles radical circle, and Lucas inner circle.
Furthermore, the common chord determined by these points also passes through the symmedian point of the original triangle (Kimberling).
