The orthocentroidal circle of a triangle 
is a central circle
having the segment joining the triangle centroid 
and orthocenter 
of 
as its diameter (Kimberling 1998, p. 234). Since
the Euler line passes through 
and 
, it therefore bisects the orthocentroidal circle.
It has circle function
 |
(1)
|
which corresponds to the circumcenter 
. The center of the circle is Kimberling
center 
,
which has equivalent triangle center functions
 |  |  |
(2)
|
 |  |  |
(3)
|
The circle has radius
 |  |  |
(4)
|
 |  |  |
(5)
|
where 
is the circumradius of 
.
The circle does not pass through any notable centers other than 
and 
, which are Kimberling centers 
and 
, respectively.
It is orthogonal to the Lester circle and Stevanović circle.
The orthocentroidal circle of any triangle always contains the incenter 
(Guinand 1984). This is an interesting observation since it means that the incenter
is always "close" to the Euler line of the
triangle (although it does not lie on it).
