Archimedean circles related to the Schoch line

Reference: Explanation:
The two red points are the centers of the two inner semicircles of the arbelos. The point of intersection
of the Schoch line (the vertical black line) and the semicircle with diameter joining the two red points have
interesting properties. There are ten Archimedean circles passing through the point (cases 1, 2, 3).
Even two squares are involved (cases 1, 2).
The case 4 demonstrates three other Archimedean circles touching the Schoch line.
Please scroll down and click the checkboxes.

Applet programmed by Kyouhei Tetsuka

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