the midpoint of the two limiting points is the point where the radical axis of "a" and "b" crosses the line through their centers. this intersection point has equal power distance to all the circles in the pencil containing "a" and "b". the limiting points themselves can be found at this distance on either side of the intersection point, on the line through the two circle centers. from this fact it is straightforward to construct the limiting points algebraically or by compass and straightedge.