Given two circles, one of radius 1, and another of radius 2, and the distance between the centers is 4, what is set of points that are equidistant from the two circles?
Now I think naturally the first thing to do is to solve an easier problem, so if one matches the radii, then the set of points that are equidistant is just a straight line that is exactly half-way in between them. I'm thinking of what happens when we increase the radius of one of them, the line somehow rotates towards the circle with the smaller radius, and the line also becomes closer to the circle of the larger radius. Is my intuition correct here?