# Circumcenter

Pronunciation: /ˈsɜr.kəmˌsɛn.tər/ Explain

 Click on the blue points and drag them to change the figure Manipulative 1 - Circumcircle of a Triangle Created with GeoGebra.

The circumcenter of a polygon is the center of the circle that intersects all vertices of the polygon exactly once. The circumcircle of a polygon is the circle that intersects all vertices of the polygon. The circumcenter of a triangle is found at the intersection of the perpendicular bisectors of the sides. A circumradius of a polygon is a radius of the circumcircle.

### How to Construct the Circumcenter and Circumcircle of a Triangle

 1 Pick any one side of a triangle and construct its perpendicular bisector. 2 Pick one of the remaining sides of a triangle and construct its perpendicular bisector. 3 Draw a circle with the center at the intersection of the two bisectors and a radius of the distance between the intersection and any vertex of the triangle.

### How to Construct the Circumcenter and Circumcircle of a Regular Polygon

StepIllustrationDiscussion and Justification
1 The center of a regular polygon is at the point of concurrency of perpendicular bisectors of any two sides that are not opposite each other.
2 Draw the perpendicular bisector of any side.
3 Draw the perpendicular bisector of any other side that is not opposite the side you used in step 2.
4 Label the intersection of the two perpendicular bisectors as 'center'.
5 Draw a circle with a center at the point labeled 'center' and the edge at any vertex. This is the circumcircle.
Table 2 - How to construct the center and circumcircle of a regular polygon

### References

1. McAdams, David E.. All Math Words Dictionary, circumcenter. 2nd Classroom edition 20150108-4799968. pg 33. Life is a Story Problem LLC. January 8, 2015. Buy the book

• McAdams, David E.. Center. allmathwords.org. Life is a Story Problem LLC. 6/27/2018. http://www.allmathwords.org/en/c/center.html.

McAdams, David E. Circumcenter. 3/5/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/circumcenter.html.

### Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/16/2018: Changed incenter to circumcenter. (McAdams, David E.)