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.

Steps

1. Find the centres of the given circles
2. The first set of points is the line h containing the given point A and the centre of the smaller circle S2
3. Draw a line g containing the given point A and the center of the larger circle S1
4. Find the intersections with the line g and the larger circle and name it D
5. Draw a point F in the middle of the line AD
6. Construct an ellipse with foci at point A and S1
7. Find the intersection of the ellipse and the line h that is not point S2 and name it G
8. Draw a circle k with centre G passing through point A