TOPICS

# Schoch Line

In the arbelos, consider the semicircles and with centers and passing through . The Apollonius circle of , and the large semicircle of the arbelos is an Archimedean circle . This circle has radius

(as it must), and center

The line perpendicular to and passing through the center of is called the Schoch line.

Now let and be two semicircles through with radii proportional to and respectively. The circle tangent to and with its center on the Schoch line is an Archimedean circle. These circles are called Woo circles.

Let be the radical axis of the great semicircle of the arbelos and . From a point on consider the tangents to the circle on diameter . The circle with center on the Schoch line and tangent to these tangents is a Woo circle (Okumura and Watanabe 2004).

An applet for investigating Woo circles and Schoch lines has been prepared by Schoch (2005).

Arbelos, Archimedes' Circles, Woo Circle

This entry contributed by Floor van Lamoen

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## References

Dodge, C. W.; Schoch, T.; Woo, P. Y.; and Yiu, P. "Those Ubiquitous Archimedean Circles." Math. Mag. 72, 202-213, 1999.Okumura, H. and Watanabe, M. "The Archimedean Circles of Schoch and Woo." Forum Geom. 4, 27-34, 2004. http://forumgeom.fau.edu/FG2004volume4/FG200404index.html.Schoch, T. "Arbelos: The Woo Circles." 2005. http://www.retas.de/thomas/arbelos/woo.html.

Schoch Line

## Cite this as:

van Lamoen, Floor. "Schoch Line." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/SchochLine.html