Constructing a regular Pentagon

There are many methods to construct a regular pentagon. Here is one method I saw on a website.
These are the sequence of steps
1. Draw a circle and its diameter
2. Draw a perpendicular to its diameter
3. The perpendicular will intersect the circle at two points, find the middle point of the radius on this
perpendicular and draw a circle.
4. Now join a line through foot of the diameter to the center of the circle and let it intersect the circle at two points.
5. Use foot of the diameter and the upper part where it crosses the circle as the radius and draw an arc which crosses the original big circle at two points. The top point of diameter and the crossing on circle gives you the measure of the side of the pentagon. Use this to find other sides using compass.

I did these steps using KSEG and also measured the sides and it came out perfect