Three Externally Tangent Circles

Steps

0. We have circles c, d and h, which are all touching externally.
1. Find points D, E and F, in which the circles intersect each other.
2. Construct 3 hyperbolas, which have their foci in the circles' centers and cross through one of the points D, E and F, which are located on the circles, whose centers are foci of hyperbolas ?
3. Find points S, where all three hyperbolas intersect.
4. Construct lines p, which intersect with an S point and one of the circles' centers and find points I and N, which are an intersection of a p line and a circle through whose center p crosses.
5. Construct circles k, which have their center in point S and also intersect either point I or N.