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Determine the locus of intersections of lines

Source: Sharygin contest 2008. The correspondence round. Problem 16

September 3, 2008
geometric transformationgeometrypower of a pointradical axisgeometry proposed

Problem Statement

(A.Zaslavsky, 9--11) Given two circles. Their common external tangent is tangent to them at points A A and B B. Points X X, Y Y on these circles are such that some circle is tangent to the given two circles at these points, and in similar way (external or internal). Determine the locus of intersections of lines AX AX and BY BY.
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