On the line AB, beginning at A and going in the opposite sense to B we draw a segment AAb having the same length as side BC.
On the line AC, beginning at A and going in the opposite sense to C we draw a segment AAc having the same length as side BC.
We do the same with the other two vertices and obtain four more points Ba, Bc, Ca and Cb. The six points Ab, Ac, Ba, Bc, Ca and Cb lie in a circle called the Conway circle of ABC. Its center is the incenter I.

Conway_circle.mac