Without Contact

Steps

1. Draw a circle for a circular inversion with a centre in point A.
2. Invert line f and circle k according to the circle of the circular inversion. Point A will be displayed indefinitely.
3. Find common tangents of displayed circles.
4. Display the tangents from step 3 over the circle of the circular inversion.
5. You have a solution!

Steps

1. Create a line p₂ that will pass through the center of S₁ and the given point A. Name the intersection of the circle k₁ and the line p₂ closer to point A B and find the center C between points A and B.
2. Draw a perpendicular line p₃ that is perpendicular to the line p₁ and passes through the given point A.
3. Find points equidistant from the circle k₁ and point A. Thus, we are looking for a hyperbola e with foci at points A and S₁ that passes through point C.
4. We look for points equidistant from the line p₁ and point A. Thus, we are looking for a parabola g with a control line p₁ and foci at point A.
5. Name the intersections of the hyperbola e and the parabola g S.
6. The points S are the centres of the circles we are looking for. They must all pass through point A.