Pentagon

Inscribed in a Circle
1. Begin with a circle centered on O with point A on it.

2. Construct the line $$\overset{\longleftrightarrow}{A O}$$. It intersects $$\overset{\frown}{O A}$$ at point B.

3. Construct the perpendicular bisector of $$\overline{A B}$$. It intersects $$\overset{\frown}{O A}$$ at point C.

4. Construct the midpoint M of $$\overline{C O}$$.

5. Construct the circle $$\overset{\frown}{M O}$$.

6. Construct the ray $$\overrightarrow{B M}$$. It intersects $$\overset{\frown}{M O}$$ at points D and E.

7. Construct the circles $$\overset{\frown}{B D}$$ and $$\overset{\frown}{B E}$$. They intersect $$\overset{\frown}{O A}$$ at points F, G, H and I.

8. Construct the line segments $$\overline{A G}$$, $$\overline{G H}$$, $$\overline{H I}$$, $$\overline{I F}$$ and $$\overline{F A}$$.

From a Given Side Length
1. Begin with a line segment $$\overline{A B}$$

2. Construct the perpendicular bisector of $$\overline{A B}$$. They intersect at point M.

3. Extend the line $$\overset{\longleftrightarrow}{A B}$$ and construct circle $$\overset{\frown}{A M}$$. They intersect at point C.

4. Construct the circle $$\overset{\frown}{M C}$$. It intersects the perpendicular bisector at point D.

5. Construct the ray $$\overrightarrow{D A}$$. It intersects the circle $$\overset{\frown}{A M}$$ on the far side at point E.

6. Copy the distance $$\overline{D E}$$. Construct circles of that radius centered on points A and D. They intersect at point F.

7. Copy the distance $$\overline{A B}$$. Construct a circle of that radius on point F. It intersects the circles $$\overset{\frown}{A F}$$ and $$\overset{\frown}{B F}$$ and points G and H.

8. Construct the line segments $$\overline{A G}$$, $$\overline{G F}$$, $$\overline{F H}$$ and $$\overline{F B}$$.