What is an arbelos?
Properties of an arbelos
        Distances and areas
        Archimedes' circles
        Apollonius circle
        Bankoff circle
        Pappus chain

Stephen Tan
Dec 16, 2005
Math 308 by Dr. Bill Casselman
Final Project
Page 10
Let B be the point at the notch of the arbelos, and D directly above it on the enclosing semicircle. Let MM' be a perpendicular bisector of AC, and let E and G be points sitting at the top of the interior semicircles.
Let EG intersect MM' and BC at I and J respectively. Then circles C6 - passing through I and tangent to arc AC at M' - and C6' - passing through J and tangent to arc AC at Pc - and C6'' - passing through J and tangent to AC at B - are all Archimedean circles.
The circle C6'' is also known as a Bankoff circle.
The centers of C6, C6', C6'' are given by

Rather amazing, E, M, B, G, Pc, D, and M' are concyclic in a circle with center at ((1 + 2r)/4 , 1/4) and radius