Hello,

all points R form a circle which contains the points A and B too. (see attachment)

Construction:

1. draw AB

2. draw the perpendicular bisector of AB

3. draw the angle (here 45°) with the perp. bisector as one leg and the other leg of the angle has to pass either through A or B (I've taken A. blue angle)

4. the vertex of the angle is the centre of the above mentioned circle.

5. draw the circle: The radius is the distance centre-A or centre-B

To demonstrate I've added a few points R which form angles of 45° together with A and B.

EB