Two Circles With Inner Contact, Point Between The Circles

Steps

-5. We have two internally tangent circles and a point A lying between them.
-4. Draw any circle e with its center at point A.
-3. Use a circle inversion to map the circles given in the problem inside circle e.
-2. Draw tangents to the new circles from the point 3.
-1. Use a circle inversion to map these tangents outside circle e.
0. The resulting circles are the solution to the problem.