Three Intersecting Circles

Steps

1. Construct three hyperbolas whose foccuses are at the centres of the circles and which pass through their intersection.
2. Construct two ellipses whose foccuses are at the centers of the given circles and which pass through their intersection (can be done with any circle from the given set).
3. Two intersections of three hyperbolas are two solutions, different intersections of hyperbolas and ellipses hide 6 more solutions.
4. We havae 8 solutions