Square

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

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

3. Construct the perpendicular bisector of $$\overline{A B}$$. It intersects the circle at C and D.

4. Construct the segments $$\overline{A C}$$, $$\overline{A D}$$, $$\overline{B C}$$ and $$\overline{B D}$$.

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

2. Construct lines perpendicular to $$\overline{A B}$$ that pass through A and B.

3. Construct the circles $$\overset{\frown}{A B}$$ and $$\overset{\frown}{B A}$$. They intersect the perpendicular lines at C and D.

4. Construct the segment $$\overline{C D}$$