Archimedean circles of the collinear arbelos and the skewed arbelos (Q2856397)

For a point \(O\) on the segment \(AB\) in the plane, the area surrounded by the three semicircles with diameters \(AO\), \(BO\) and \(AB\) erected on the same side is called an arbelos. The radical axis of the inner semicircles divides the arbelos into two curvilinear triangles with congruent incircles called the twin circles of Archimedes. Circles congruent to these circles are said to be Archimedean. The arbelos can be generalized in three ways, the collinear arbelos of intersecting type, the collinear arbelos of non-intersecting type and the skewed arbelos. The author gives several constructions for Archimedean circles of the collinear arbelos. He also defines Archimedean circles of the skewed arbelos by generating the twin circles of Archimedes of the ordinary case and shows some examples of such Archimedean circles.