Conway circle theorem

In plane geometry, the Conway circle theorem states that when the sides meeting at each vertex of a triangle are extended by the length of the opposite side, the six endpoints of the three resulting line segments lie on a circle whose centre is the incentre of the triangle. The circle on which these six points lie is called the Conway circle of the triangle.[1][2][3] The theorem and circle are named after mathematician John Horton Conway.

A triangle's Conway circle with its six concentric points (solid black), the triangle's incircle (dashed gray), and the centre of both circles (white); solid and dashed line segments of the same colour are equal in length