Circles with Internal Tangency, Line Tangent to Inner Circle

Steps

1. Construct the circle of inversion. Choose the point of tangency T as its center.
2. Apply the inversion to the given objects. In the chosen inversion, the given line remains invariant. One of the given circles is transformed into a line parallel to it.
3. Identify the images of the solutions. The first three are circles located in the strip between the two parallel lines. The fourth is a tangent to the image of the circle, which is parallel to both lines. The image of the point of tangency with the remaining two objects lies at infinity.
4. Apply the inverse transformation to the found circles and line.
5. The problem has four solutions.