# Circle (A_{15}): The Schoch segment Circle

### Definition

Let P be on the circle with diameter O_{1}O_{2} and be the center of a circle tangent to both (O_{1})
and (O_{2}). Let P' be the perpendicular foot of P on BC. We call PP' the Schoch segment, and the circle with the
Schoch segment as diameter is the Archimedean circle (A_{15}) [Dodge e.a. 1999].

### Remark

The circle (P) is congruent to the circle passing through C and the points where (P) is tangent to (O_{1})
and (O_{2}) [FvL, 21 Oct 2006].

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