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 .