Two Concentric Circles

Steps

1. Draw a line passing through the common center of the given circles and the intersections of the line with circles A, B, C.
2. Points C₁ and C₂ are the centers of the segments AB and AD. These two points represent the centers of the circles we are looking for. The circle centered at C₁ will have an external tangent with circle k₁, and the circle centered at C₂ will have an internal tangent.
3. Draw circles centered at point S that pass through points C₁ and C₂.
4. The resulting circles are the desired set of points.