Two Circles With Inner Contact, Point On The Smaller Circle

Steps

0. Given are the circles a and b such that a is internally tangent to b. Also given is the point A, which lies on a and is not the tangent point of the two circles.
1. Draw any circle c with A as its origin.
2. Invert this circle. Point A' is now at infinity. The inverted forms of a and b shall be named a' and b' respectively.
3. Now, construct the line d that is tangent to b' and parallel to a'. This line must touch a' and go through A' in infinity.
4. Invert d around c. The resulting circle is the solution.