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compass and straightedge construction of center of given circle

Given a circle in the Euclidean plane, one can construct its center using compass and straightedge as follows:

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

$\begin{pspicture}(-4,-4)(4,4) \rput[r](3,0){.} \rput[a](0,3){.} \rput[l](-3,0){.... ...$} \rput[a](2.5981,-1.8){$B$} \psdots(-2.5981,-1.5)(2.5981,-1.5) \end{pspicture}$
Construct the perpendicular bisector of $\overline{AB}$ in order to find the two points $C$ and $D$ where it intersects the circle.

$\begin{pspicture}(-4,-4)(4,4) \rput[r](3,0){.} \rput[a](0,4){.} \rput[l](-3,0){.... ...[r](-0.1,3.2){$D$} \psdots(-2.5981,-1.5)(2.5981,-1.5)(0,-3)(0,3) \end{pspicture}$
Construct the perpendicular bisector of $\overline{CD}$ to determine the midpoint $O$ of $\overline{CD}$ . $O$ is the center of the circle.

$\begin{pspicture}(-4,-4)(4,4) \rput[r](4,0){.} \rput[a](0,4){.} \rput[l](-4,0){.... ...(-0.1,0){$O$} \psdots(-2.5981,-1.5)(2.5981,-1.5)(0,-3)(0,3)(0,0) \end{pspicture}$

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 link provided.

compass and straightedge construction of center of given circle is owned by Warren Buck.

How to Cite This Entry

Warren Buck. "compass and straightedge construction of center of given circle" (version 7). PlanetMath.org. Freely available at http://planetmath.org/CompassAndStraightedgeConstructionOfCenterOfGivenCircle.html.

AMS MSC:	51-00 (Geometry :: General reference works (handbooks, dictionaries, bibliographies, etc.))
	51M15 (Geometry :: Real and complex geometry :: Geometric constructions)

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