arbelos
What is an arbelos?
Properties of an arbelos
Distances and areas
Archimedes' circles
Apollonius circle
Bankoff circle
Pappus chain
References
Stephen Tan
42373027
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 C_{6}  passing through I and tangent to arc AC at M' 
and C_{6}'  passing through J and tangent to arc AC at P_{c} 
and C_{6}''  passing through J and tangent to AC at B 
are all Archimedean circles.
The circle C_{6}'' is also known as a Bankoff circle.
The centers of C_{6}, C_{6}', C_{6}'' are given by
Rather amazing, E, M, B, G, P_{c}, D, and M' are concyclic in a circle with center at
((1 + 2r)/4 , 1/4) and radius


