What is an arbelos?
Properties of an arbelos
Distances and areas
Dec 16, 2005
Math 308 by Dr. Bill Casselman
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