Hexagon

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

2. Construct the circle $$\overset{\frown}{A O}$$. It intersects $$\overset{\frown}{O A}$$ at points B and C.

3. Construct the circles $$\overset{\frown}{B O}$$ and $$\overset{\frown}{C O}$$. They intersect $$\overset{\frown}{O A}$$ at points D and E.

4. Construct the circle $$\overset{\frown}{E O}$$. It intersects $$\overset{\frown}{O A}$$ at points F.

5. Construct the line segments $$\overline{A B}$$, $$\overline{B D}$$, $$\overline{D F}$$, $$\overline{F E}$$, $$\overline{E C}$$ and $$\overline{C A}$$.

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

2. Construct the circles $$\overset{\frown}{A B}$$ and $$\overset{\frown}{B A}$$. They intersect at point O.

3. Construct the circle $$\overset{\frown}{O A}$$. It intersects the other circles at points C and D.

4. Construct the circles $$\overset{\frown}{C O}$$ and $$\overset{\frown}{D O}$$. The intersect circle $$\overset{\frown}{O A}$$ at points E and F.

5. Construct the line segments $$\overline{A C}$$, $$\overline{C E}$$, $$\overline{E F}$$, $$\overline{F D}$$ and $$\overline{D B}$$.