How to Circumscribe a Circle About a Triangle

StepExampleDescription
1Triangle ABCStart with triangle ΔABC.
2Triangle ABC with perpendicular bisector of side AB.Draw a perpendicular bisector of one of the sides. In this case, the perpendicular bisector of AB is drawn.
3Triangle ABC with perpendicular bisector of side BC.Draw a perpendicular bisector of another side. In this case, the perpendicular bisector of BC is drawn.
4Triangle ABC with intersection of the perpendicular bisectors labeled point D.Label the intersection of the perpendicular bisectors as point D.
5Triangle ABC with circumscribing circle drawn with center D and radius DA.Draw a circle with center D and radius DA.

Checkmark Understanding Check

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

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  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 side AB. You have constructed the first perpendicular bisector.
  2. Repeat step one to draw the second perpendicular bisector to any of the other two 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 D 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 D, the circumcenter and one of the vertices of the triangle. 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 1: Circumscribing a circle about a triangle.

Cite this article as:
How to Circumscribe a Circle About a Triangle. 2008-07-03. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/h/htcircumscribetriangle.html.

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2008-07-03: Initial version (McAdams, David.)

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