Given are the points A and B in the plane. If x is a straight line is in that plane, and x does not coincide with the perpendicular bisectror of AB, then denote the number of points C located at x such that △ABC is isosceles, as the "weight of the line x”.
Prove that the weight of any line x is at most 5 and determine the set of points P which has a line with weight 1, but none with weight 0. geometryisoscelescombinatorial geometry