Two Circles With Inner Contact, Point On The Common Point

Steps

0. Given are the circles a and b that are touching internally. The tangent point of the two is the given point A.
1. Construct the line p that goes through A and centres of both a and b. All points on line p are possible centres of the solution.
2. Choose any point on the line. Draw a circle that has this point as its center and passes through the point A. That is one of the infinitely many solutions.