Arbelos

Peter Y. Woo discovered an infinite number of Archimedean circles [5] centered on the Schoch line [18] by generalizing the Schoch circles W15 and W16 [3].

Chose any nonnegative real number m.

Draw two circles (magenta) centered on the arbelos ground line (blue) tangent to each other in point C (blue), and with radius m times the radius of the corresponding small arbelos arc.

The circle (red) centered on the Schoch line and externally tangent to these circles is a Woo circle.

The applet above has two draggable points. The blue one is point C and can be moved along the arbelos ground line.

The red one is used to adjust the radius multiplier m, the value of which is displayed bottom left. (The scale may help at this.)

Even though the value of m may be zero (the Woo circle then is circle W11), its upward movability is limited to prevent the draggable points from overlapping.

The applet starts with the radius multiplier set to 2, and the Woo circle is Schoch circle W15. Setting it to 1 the Woo circle will be Schoch circle W16.

Circle numbering is taken from [3].