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Determine the locus of points

Source: Sharygin contest 2008. The correspondence round. Problem 6

September 3, 2008
geometry proposedgeometry

Problem Statement

(A. Myakishev, 8--9) In the plane, given two concentric circles with the center A A. Let B B be an arbitrary point on some of these circles, and C C on the other one. For every triangle ABC ABC, consider two equal circles mutually tangent at the point K K, such that one of these circles is tangent to the line AB AB at point B B and the other one is tangent to the line AC AC at point C C. Determine the locus of points K K.
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