Describe a circle ABC (Figs. 1 and 2). Draw two chords AB, BC intersecting within it. Describe eight circles (a, a′ b, b′, etc.), each of which touches ABC and the chords AD, BC; construct a triangle by joining any three of the points of intersections of ABC and the two chords; then the chords of contact and the line of centres of two circles taken in suitable pairs out of the eight circles are concurrent, the point of concurrence being equidistant from the three sides of the triangle.