Circles with Internal Tangency, External Line Tangent

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 is a circle located in the strip between the two parallel lines. The second is a tangent to the image of the original 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 identified circle and line.
5. The problem has two solutions.