circle with given center and given radius
Task. Draw the circle having a given point O as its center and a given line segment 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. (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.
Solution.
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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.
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2.
Draw the lines ↔CA and ↔CO.
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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.
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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 E≠C.
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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.
References
- 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 |