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.
With centre C, draw a circle of radius $\displaystyle CA_i=CA_j$.
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.