Let A(C) be the circle through C with center A, and A' the reflection of C through A. The circle with center on AB and tangent to the radical line of A(C) and (O) and also tangent to the tangent from A' to B(C) is Archimedean. Similarly the circle with center on AB and tangent to the radical line of B(C) and (O) and also tangent to the tangent from B' to A(C) is Archimedean [van Lamoen 2006].