How to construct the locus of a point R which moves such that angle ARB = 45 degrees and the distance of AB is fixed.
all points R form a circle which contains the points A and B too. (see attachment)
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.