compass and straightedge construction of center of given circle

Given a circle in the Euclidean plane, one can construct its center (http://planetmath.org/Center8) using compass and straightedge as follows:

1. Draw a chord. Label its endpoints as $A$ and $B$.

2. Construct the perpendicular bisector of $\overline{AB}$ in order to find the two points $C$ and $D$ where it intersects the circle.

3. Construct the perpendicular bisector of $\overline{CD}$ to determine the midpoint $O$ of $\overline{CD}$. $O$ is the center of the circle.

A justification for these constructions is supplied in the entry construct the center of a given circle.

If you are interested in seeing the rules for compass and straightedge constructions, click on the provided.