How to construct the locus of a point R which moves such that angle ARB = 45 degrees and the distance of AB is fixed.

Many thanks!

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- Jan 31st 2007, 10:40 PMacc100jtconstructing locus
How to construct the locus of a point R which moves such that angle ARB = 45 degrees and the distance of AB is fixed.

Many thanks! - Feb 1st 2007, 01:59 AMearboth
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