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
Step  Illustration  Discussion 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
 McAdams, David E.. All Math Words Dictionary, circumcenter. 2nd Classroom edition 201501084799968. pg 33. Life is a Story Problem LLC. January 8, 2015. Buy the book
More Information
 McAdams, David E.. Center. allmathwords.org. Life is a Story Problem LLC. 6/27/2018. https://www.allmathwords.org/en/c/center.html.
Cite this article as:
McAdams, David E. Circumcenter. 3/5/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/c/circumcenter.html.
Image Credits
Revision History
3/5/2019: Added word links. (
McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (
McAdams, David E.)
12/16/2018: Changed incenter to circumcenter. (
McAdams, David E.)
6/25/2018: Removed broken links, updated license, implemented new markup, updated GeoGebra apps. (
McAdams, David E.)
4/28/2011: Added circumradius. (
McAdams, David E.)
10/13/2010: Generalize article to deal with all polygons, rather than just triangles. Added section on constructing the circumcenter and circumcircle of a regular polygon. (
McAdams, David E.)
1/9/2010: Added "References". (
McAdams, David E.)
11/15/2008: Changed manipulative to Geogebra. (
McAdams, David E.)
7/7/2008: Corrected link errors. Corrected spelling (
McAdams, David E.)
3/25/2008: Revised More Information to match current standard. (
McAdams, David E.)
8/24/2007: Simplified figure 1. Added reference to triangle. Added circumcircle (
McAdams, David E.)
7/30/2007: Initial version. (
McAdams, David E.)