Draw the perpendicular line from the intersection of the two small semicircles
in the arbelos. The two circles 
and 
tangent to this line, the large
semicircle, and each of the two semicircles
are then congruent and known as Archimedes' circles.
For an arbelos with outer semicircle of unit radius and parameter 
, Archimedes' circles have radii
 |
(1)
|
and centers
 |  |  |
(2)
|
 |  |  |
(3)
|
Circles that are constructed in a natural way using an arbelos and are congruent to Archimedes' circles are known as Archimedean circles.
