Hart Circle
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).
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