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[parent] compass and straightedge construction of center of given circle (Algorithm)

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

  1. 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}
  2. 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}
  3. 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.



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Cross-references: compass and straightedge constructions, construct the center of a given circle, midpoint, intersects, points, perpendicular bisector, endpoints, chord, straightedge, compass, Euclidean plane, circle
There are 2 references to this entry.

This is version 7 of compass and straightedge construction of center of given circle, born on 2007-06-09, modified 2007-06-13.
Object id is 9556, canonical name is CompassAndStraightedgeConstructionOfCenterOfGivenCircle.
Accessed 968 times total.

Classification:
AMS MSC: 51-00 (Geometry :: General reference works )
 51M15 (Geometry :: Real and complex geometry :: Geometric constructions)
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