Schoch line

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In geometry, the Schoch line was created by Thomas Schoch.

[edit] Construction

With an arbelos two circular arcs K₁ and K₂ are created with the centers at point A and C, respectively. 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, hence it is called "Archimedean". 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.

[edit] Radius and center of A₁

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

and the center is

[edit] References

• van Lamoen, Floor. Schoch Line." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. Retrieved on 2008-04-11.