Conway’s Circle Theorem: a short proof, enabling generalization to polygons

Conway’s Circle Theorem: a short proof, enabling generalization to polygons Braude, Eric John Conway’s Circle Theorem is a gem of plane geometry: the six points formed by continuing the sides of a triangle beyond every vertex by the length of its opposite side, are concyclic. The theorem has attracted several proofs, even adorned Mathcamp T-shirts. We present a short proof that views the extended sides as equal tangents of the incircle, a perspective that enables generalization to polygons.