﻿ How to Circumscribe a Circle About a Rectangle: How to circumscribe a circle about a rectangle using a compass and a straight edge.

# How to Circumscribe a Circle About a Rectangle

Pronunciation: /ˈsɜr kəmˌskraɪb/ ?
StepExampleDescription
2Draw 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.
3Draw midpoint of an adjacent side. In this case, the midpoint of BC is drawn. Label the midpoint F.
4Draw a line through E perpendicular to AB.
5Draw a line through F perpendicular to BC.
6Label the intersection of the two perpendicular lines G.
7Draw a circle with center at G and radius of GA.

#### 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 to open the line menu. Select the Line Bisector 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 . Select the Intersect Two Objects 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 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 menu button. Then click on the blue points and drag them to change the figure.

Table 2: Circumscribing a circle about a rectangle.

• 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.

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.

### Revision History

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