How to Circumscribe a Circle About a Rectangle

Pronunciation: /ˈsɜr kəmˌskraɪb/ ?
StepExampleDescription
1Rectangle ABCDStart with rectangle ABCD.
2Rectangle ABCD with midpoint E of segment AB.Draw the midpoint of one of the sides. In this case, the midpoint of AB is drawn. Label the midpoint E. See Bisecting a Line Segment for information on finding the midpoint of a line segment and drawing the perpendicular bisector of a line segment.
3Rectangle ABCD with midpoint D of segment BC.Draw midpoint of an adjacent side. In this case, the midpoint of BC is drawn. Label the midpoint F.
4Rectangle ABCD with line through E perpendicular to AB.Draw a line through E perpendicular to AB.
5Rectangle ABCD with line through F perpendicular to BC.Draw a line through F perpendicular to BC.
6Rectangle ABCD with intersection of two perpendicular lines labeled G.Label the intersection of the two perpendicular lines G.
7Rectangle ABCD with a circle with center G and radius GA.Draw a circle with center at G and radius of GA.

Checkmark Understanding Check

Use the GeoGebra application below to construct the circumscribing circle about the rectangle.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
  1. Click on the down arrow of the line button GeoGebra line button. to open the line menu. Select the Line Bisector GeoGebra line bisector menu item. menu item. Then click on any side. You have constructed the first perpendicular bisector.
  2. Repeat step one to draw the second perpendicular bisector to any of the two adjacent sides.
  3. Click on the down arrow of the Point menu button Geogebra point menu button.. Select the Intersect Two Objects Geogebra intersect two objects menu button menu button. Click on each of the two perpendicular bisectors. Point E that appears at the intersection of the two angle bisectors is the circumcenter.
  4. Click on the Circle from Two Points Geogebra circle from two points menu button. menu button. Click on point E, the circumcenter and one of the vertices of the rectangle. The circle that appears is the circumcircle.

To change the manipulative, first click on the arrow GeoGebra arrow button. menu button. Then click on the blue points and drag them to change the figure.

Table 2: Circumscribing a circle about a rectangle.

More Information

  • McAdams, David. How to Circumscribe a Circle About a Rectangle. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 2010-01-11. http://www.allmathwords.org/article.aspx?lang=en&id=Circumscribing a Circle About a Rectangle.

Cite this article as:


How to Circumscribe a Circle About a Rectangle. 2010-01-11. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/h/htcircumscriberectangle.html.

Translations

Image Credits

Revision History


2010-01-11: Added reference to drawing the perpendicular bisector of a line segment. (McAdams, David.)
2008-07-03: Initial version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License