Let 
, 
, and 
be the side lengths of a reference
triangle 
.
Now let 
be a point on the extension of the segment 
beyond 
such that 
. Similarly, define the points 
, 
, 
, 
, 
so that the points 
and 
lie on the extended segment 
, the points 
and 
lie on the extended segment 
, and the point 
lies on the extended segment 
, and we have 
, 
, 
, 
and 
.
Then the points 
,
, 
, 
, 
, and 
are concyclic and the resulting
circle is known as Conway circle of 
.
The Conway circle is centered at the incenter 
of the reference triangle 
and has radius
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the inradius of the reference
triangle and 
its semiperimeter.
It has circle function
 |
(3)
|
corresponding to Kimberling center 
.
No Kimberling centers lie on the Conway circle.
