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.
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 K<sub>1</sub> and K<sub>2</sub> 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 K<sub>3</sub> be the largest of the three arcs of the arbelos. A circle, with the center A<sub>1</sub>, is then created tangent to the arcs K<sub>1</sub>, K<sub>2</sub>, and K<sub>3</sub>. 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 A<sub>1</sub>. It is also the location of the centers of infinitely many Archimedean circles, e.g. the Woo circles.
If r = AB/AC, and AC = 1, then the radius of A<sub>1</sub> is
and the center is