The circle 
which touches the incircles 
, 
, 
,
and 
of a circular
triangle 
and its associated triangles. It is either
externally tangent to 
and internally tangent to incircles of the associated
triangles 
,
, and 
(as in the above figure), or vice versa. The Hart circle
has several properties which are analogous to the properties on the nine-point
circle of a linear triangle. There are eight Hart circles associated with a given
circular triangle.
The Hart circle of any circular triangle and the Hart circles of the three associated triangles have a common tangent circle which touches the former in the opposite sense to that which it touches the latter (Lachlan 1893, p. 254). In addition, the circumcircle of any circular triangle is the Hart circle of the circular triangle formed by the circumcircles of the inverse associated triangles (Lachlan 1893, p. 254).
