Circle (A15): The Schoch segment Circle

Definition

Let P be on the circle with diameter O1O2 and be the center of a circle tangent to both (O1) and (O2). 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 (A15) [Dodge e.a. 1999].

Remark

The circle (P) is congruent to the circle passing through C and the points where (P) is tangent to (O1) and (O2) [FvL, 21 Oct 2006].


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