Circumscribing a Circle About a Regular Polygon

Pronunciation: /ˈsɜr kəmˌskraɪb/ ?
StepExampleDescription
1Hexagon ABCDEFStart with hexagon ABCD.
2Hexagon ABCDEF with perpendicular bisector of EF.Draw the perpendicular bisector of one of the sides. In this case, the perpendicular bisector of EF is drawn.
3Hexagon ABCDEF with perpendicular bisector of ED.Draw the perpendicular bisector of one of the other sides of the hexagon which is not opposite the last side used. In this case, the perpendicular bisector of BC is drawn.
4Hexagon ABCDEF with point G labeled.Label the point at the intersections of BC and EF. This is the circumcenter.
5Hexagon ABCDEF with circumcircle.Draw a circle with center at G and edge at any of the vertices. This is the circumcircle.

CheckmarkUnderstanding 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 constructor 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 side that is not opposite the first side used.
  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 G 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 G, the circumcenter and any one of the vertices of the polygon. 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 regular polygon.

Cite this article as:


Circumscribing a Circle About a Regular Polygon. 2008-07-05. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/h/htcircumregpolygon.html.

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2008-07-05: Initial version (McAdams, David.)

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