Constructing the
T R I A N G L E
and the
H E X A G O N

Inscribing an equilateral triangle in a circle.
Start with a circle O. Choose any random point P on circle O. From P construct a circle with radius PO. The circle you just made will intersect circle O at A and B. Construct a circle centered at B. Circle B will intersect circle O at P2. Construct a circle centered at P2. Circle P2 intersects circle O at C. Points A,B,C are the points of the triangle.
Or you can just construct a circle, keep the radius and draw another circle. From the intersection draw another circle, and another circle. 

If you keep doing this you will eventually get a hexagon. If you bisect one of the sides, you can construct a dodecagon (12-gon).

Lets say you were given a side and was asked to construct a hexagon with that side. First, construct two circles on each end of the segment with a radius equal to the segment. Draw another circle at the point of intersection with a radius equal to the segment. This is the circle the hexagon is to be inscribed in.

© 2002 Robin Hu