SHARYGIN 2008 Problem 6

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