Concentric Circles, Line Tangent to Outer Circle

Steps

1. The centers of the desired circles lie on the line passing through the tangency point of the given line and circle, as well as the common center of the two given concentric circles. This line is perpendicular to the given line.
2. Find the intersections of this line with the smaller of the two concentric circles.
3. The centers of the solution circles lie at the midpoints of the segments whose endpoints are the found intersection points and the point of tangency between the given line and the circle.
4. The problem has two solutions.