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A variety of methods are known for constructing a regular pentagon. The top panel shows the construction used in Richmond’s method to create the side of the inscribed pentagon. The circle defining the pentagon has unit radius. Consequently, this construction of the pentagon is valid. This methodology leads to a procedure for constructing a regular pentagon. Draw a horizontal line through the center of the circle.

Construct a vertical line through the center. It intersects the original circle at two of the vertices of the pentagon. The fifth vertex is the rightmost intersection of the horizontal line with the original circle. Construct point F as the midpoint of O and W. Construct a vertical line through F. The third vertex is the rightmost intersection of the horizontal line with the original circle. Construct the other two vertices using the compass and the length of the vertex found in step 7a.