Prove that the two circles inscribed in the two parts ACD and BCD of arbelos are equal.
(Archimedes twin circles)
Give a simple construction of these circles.
We may continue inscribing successive circles in arbelos and define
a sequence of incircles : the Pappus chain.
All the centers of these circles lie on an ellipse, for a given arbelos.
At last, choosing a fixed rank k, the locus of the center of the kth circle in the Pappus chain is an ellipse when C varies.
The case k=1 (The 1st inscribed circle) is then a specific case of a general property in all circles of the Pappus chain.
Other properties on incircle : Details (applet)