﻿ Circumcenter: The center of a circle that intersects all vertices of a regular polygon.

Circumcenter

Pronunciation: /ˈsɜr kəmˌsɛn tər/ ?

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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 incenter 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 Center 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

• McAdams, David. Center. allmathwords.org. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Center.
• McAdams, David. Circle. allmathwords.org. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Circle.
• McAdams, David. Triangle. allmathwords.org. Life is a Story Problem LLC. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Triangle.

Circumcenter. 2011-04-28. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/c/circumcenter.html.