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Math Help - Geometry

  1. #1
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    Question Geometry

    Let P be a regular n-gon, vertices A1, A2.....An. Define the centre P to be the point C such that the distance

    CAi=CAj for all i,j

    a) Prove that if a regular n-gon can be constructed then a regular (2n)-gon can be constructed.
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  2. #2
    MHF Contributor
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    With centre C, draw a circle of radius CA_i=CA_j.

    All vertices of the n-gon lie on this circle circumference.

    Draw lines from C through the midpoint of all n-gon sides
    and locate the points of intersection of all these lines with the
    circle circumference.
    Using these new points as aditional vertices, you now have a 2n-gon.
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