circle with given center and given radius

Task.  Draw the circle having a given point O as its center and a given line segmentMathworldPlanetmath of length AB as its radius. This construction must be performed with constraints in the spirit of Euclid: One must not take the length of AB¯ between the tips of the compass (i.e. (, one must pretend that the compass is collapsible ( This means than one may only draw arcs that are of circles with the center and one point of the circumferenceMathworldPlanetmath known.



  1. 1.

    Draw an arc of the circle a through A with center O and an arc of the circle o through O with center A. These arcs must intersect each other. Let one of the intersection points be C.

  2. 2.

    Draw the lines CA and CO.

  3. 3.

    Draw an arc of the circle b through B and with center A. Let D be the intersection point of b and the line CA.

  4. 4.

    Draw an arc of the circle c through C and with center D. Let E be the intersection point of d and the line CO with EC.

  5. 5.

    Draw the circle e through E and with center O. This is the required circle.


A justification for this construction is that OE=CE-CO=CD-CA=AD=AB.

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


  • 1 E. J. Nyström: Korkeamman geometrian alkeet sovellutuksineen.  Kustannusosakeyhtiö Otava, Helsinki (1948).
Title circle with given center and given radius
Canonical name CircleWithGivenCenterAndGivenRadius
Date of creation 2013-03-22 17:14:03
Last modified on 2013-03-22 17:14:03
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 30
Author Wkbj79 (1863)
Entry type Algorithm
Classification msc 51M15
Classification msc 51-00