Circles (A5a) and (A5b): The cousin circles


In the smaller arbelos semicircles (O1) and (O2) make new arbeloi similar to the original. The greater semicircle in the smaller of these arbeloi and the smaller semicircle in the greater of these arbeloi are Archimedean [Dodge et al 1999].



The first property mentioned can be extended to a property of the infinite set of Archimedean circles through C. This generalization is: A circle through C not tangent to (O1) is Archimedean if and only if the two common tangents of this circle and (O1) meet on (O2)  (here (O1) and (O2)  are taken as complete circles). [Okumura and Watanabe 2007]

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