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Math Help - constructing locus

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    constructing 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!
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    Quote Originally Posted by acc100jt View Post
    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!
    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
    Attached Thumbnails Attached Thumbnails constructing locus-puz_45.gif  
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