Two Circles, Outside Each Other

Steps

1. Draw a line through the centres of the given circles.
2. Draw the intersections on the side of the circles closer together. Draw the midpoint of these two points.
3. Draw a hyperbola with foci at the centers of the given circles that passes through the center of the points from step 2.
4. Draw the intersection of the line from step one on the far side of one circle. Use the point from step 2 on the other circle. Draw the midpoint between the two points.
5. Draw a hyperbola with foci at the centers of the given circles that passes through the center of the points from step 4.