1. Construction

2. Radius and center of A₁

3. References

4. Further reading

5. External links

In geometry, the Schoch line is a line defined from an arbelos and named by Peter Woo after Thomas Schoch, who had studied it in conjunction with the Schoch circles.

Construction

An arbelos is a shape bounded by three mutually-tangent semicircular arcs with collinear endpoints, with the two smaller arcs nested inside the larger one; let the endpoints of these three arcs be (in order along the line containing them) A, B, and C. Let K₁ and K₂ be two more arcs, centered at A and C, respectively, with radii AB and CB, so that these two arcs are tangent at B; let K₃ be the largest of the three arcs of the arbelos. A circle, with the center A₁, is then created tangent to the arcs K₁,K₂, and K₃. This circle is congruent with Archimedes' twin circles, making it an Archimedean circle; it is one of the Schoch circles. The Schoch line is perpendicular to the line AC and passes through the point A₁. It is also the location of the centers of infinitely many Archimedean circles, e.g. the Woo circles.^[1]

Radius and center of A₁

If r = AB/AC, and AC = 1, then the radius of A₁ is

and the center is

^[1]

References

Further reading

• {{citation

External links

• {{citeweb|author=van Lamoen, Floor|title=Schoch Line." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein|url=http://mathworld.wolfram.com/SchochLine.html|accessdate=2008-04-11}}

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