circle with given center and given radius
Task. Draw the circle having a given point as its center and a given line segment of length as its radius. This construction must be performed with constraints in the spirit of Euclid: One must not take the length of between the tips of the compass (i.e. (http://planetmath.org/Ie), one must pretend that the compass is collapsible (http://planetmath.org/CollapsibleCompass)). This means than one may only draw arcs that are of circles with the center and one point of the circumference known.
Draw the lines and .
Draw an arc of the circle through and with center . Let be the intersection point of and the line .
Draw an arc of the circle through and with center . Let be the intersection point of and the line with .
Draw the circle through and with center . This is the required circle.
A justification for this construction is that .
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|
|Date of creation||2013-03-22 17:14:03|
|Last modified on||2013-03-22 17:14:03|
|Last modified by||Wkbj79 (1863)|