In the arbelos, consider the semicircles 
and 
with centers 
and 
passing through 
.
The Apollonius circle 
of 
, 
and the large semicircle of the arbelos is an Archimedean
circle 
.
This circle has radius
 |
(as it must), and center
 |
The line perpendicular to 
and passing through the center of 
is called the Schoch line.
Now let 
and 
be two semicircles through 
with radii proportional to 
and 
respectively. The circle tangent to 
and 
with its center on the Schoch line is an Archimedean
circle. These circles are called Woo circles.
Let 
be the radical axis of the great semicircle
of the arbelos and 
.
From a point on 
consider the tangents to the circle on diameter 
. The circle with center on the Schoch line and tangent to
these tangents is a Woo circle (Okumura and Watanabe
2004).
An applet for investigating Woo circles and Schoch lines has been prepared by Schoch (2005).
