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.

Title	compass and straightedge construction of center of given circle
Canonical name	CompassAndStraightedgeConstructionOfCenterOfGivenCircle
Date of creation	2013-03-22 17:13:44
Last modified on	2013-03-22 17:13:44
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	10
Author	Wkbj79 (1863)
Entry type	Algorithm
Classification	msc 51M15
Classification	msc 51-00
Related topic	ConstructTheCenterOfAGivenCircle