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.

Steps

1. Draw a circle k₄ with centre S₄ at the point of contact of two circles, which touches the third one.
2. Represent the given circles by the circular inversion according to k₄, resulting in the parallel lines c´ and d´ and the circle h´
3. Draw the h-axis of the resulting parallel lines.
4. Construct the circles k₅ and k₆ tangent to the two parallels and the circle h´
5. Represent the resulting circles by circular inversion to obtain the resulting solutions, circles p´ and q´.