Start
off with a circle of a size that will perfectly fit your pentagon; that is, each corner of your pentagon will touch the outside of your circle.
1
figure 1
In my circle, I have drawn two perpendicular lines which run through the center point O. Where they cross the circle, I have labeled A, X, Y and Z (A will be the top point of the pentagon, so place it accordingly).
*I have bisected line OY to find point M; that is, M is exactly halfway between O and Y.*
figure 2
Put the point
of the compass on M and extend it so the pencil touches A.
Draw an arc that crosses line XO; we will call this intersection “R”.