# 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. 1.

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

2. 2.

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

3. 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 CompassAndStraightedgeConstructionOfCenterOfGivenCircle 2013-03-22 17:13:44 2013-03-22 17:13:44 Wkbj79 (1863) Wkbj79 (1863) 10 Wkbj79 (1863) Algorithm msc 51M15 msc 51-00 ConstructTheCenterOfAGivenCircle