A Woo circle is an Archimedean circle with center on the Schoch line and tangent to certain other circles. An applet for investigating Woo circles and Schoch lines has been prepared by Schoch.

How to construct a Woo circle?

Very easy! 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.

How to use the SketchPad diagram?

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.

References:

Okumura, H. and Watanabe, M. “The Archimedean Circles of Schoch and Woo.” Forum Geom.

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