This next construction is an odd one. The first segment has nothing to do with the outcome of the pengtagon!
 First, draw segment AB and find M, the midpoint of AB.
 Draw a circle at M (purple) with radius AB.
 Draw a perpendicular line at M. This line intersects circle M (purple), at points C and D.
 Draw a circle at C, with radius CA (yellow). Draw a line through points CA (red).
 Draw a circle at A with radius AM. This circle intersects AC at E.
 Draw a circle at C with radius CD (blue).
 Draw a line perpendicular to AC. This line intersects the large circle C (blue) at points
F and G.
 Connect points FC and GC with a line. Both lines intersect the small circle C (yellow), at points
H and I. A,H,I are points of the pentagon. You can use them to find the others.

