Stanley Rabinowitz, Pseudo-incircles,
Forum Geometricorum, 6 (2006) 107--115.

Abstract: This paper generalizes properties of mixtilinear incircles. Let (S) be any circle in the plane of triangle ABC. Suppose there are circles (S_a), (S_b), and (S_c) such that each are internally tangent to (S); and (S_a) is inscribed in angle BAC (and similarly for (S_b) and (S_c). Let the points of tangency of (S_a), (S_b), and (S_c) with (S) be X, Y, and Z, respectively. Then it is shown that the lines AX, BY, and CZ meet in a point.

[ps file][pdf file]