You get interesting special cases of the construction presented on the last page when you snap the centre K of the circle k to the perpendicular bisector of [AB]:

1. When this drawing comes near the case "k is running through A and B", then the situation becomes rather unstable. But if you try long enough, you may get the idea that in the exact case "k is running through A and B", the locus line may be a circle.
   Construct an own drawing that illustrates this special case. What circle seems the locus line to be? Can you prove your assumption?
   
   
2. Generally, when do you expect to get a locus line in axial symmetry? Be cautious, it's not just that the producing construction itself should be symmetric!