Circle And Line Without Contact

Steps

1. Through the centre of the circle k (point S), draw a perpendicular line f to the line p which intersects it at point C.
2. Construct a circle c centred at C with the same radius as k.
3. Construct parallel lines g and h to the line p, which pass through the points E and F, the intersections of f and c.
4. Construct a hyperbola d with focus S and controlling line g and a hyperbola e with focus S and controlling line h. On these hyperbolas lie the centers of all circles tangent to k and p.