Perpendicular Bisector Concurrence Theorem

Pronunciation: /ˌpɜr.pənˈdɪk.jə.lər ˈbaɪ.sɛk.tər kənˈkɜr.əns ˈθɪər.əm/ Explain

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In what cases is the point of concurrency inside the triangle. In what cases is the point of concurrency outside the triangle. In what cases is the point of concurrency on the perimeter of the triangle?
Manipulative 1 - Perpendicular Bisector Concurrence Theorem Created with GeoGebra.

The Perpendicular Bisector Concurrence Theorem proves that, for all triangles, the perpendicular bisectors of the sides of a triangle are concurrent at the circumcenter of the triangle. If one draws any triangle, then draws the perpendicular bisectors of the sides, all three perpendicular bisectors will meet at the same point. When two or more lines meet at the same point, they are said to be concurrent at that point. Furthermore, if one draws a circle with the center at the point of concurrency and the edge through any of the vertices of the triangle, it will also pass through the other two vertices. This circle is called the circumcircle of the triangle. For a proof of the Perpendicular Bisector Concurrence Theorem, see Proving the Concurrency of the Perpendicular Bisectors of a Triangle, By Sharon K. O’Kelley.


  1. Durell, Clement V.. A Concise Geometry. pg 97. G. Bell and Sons, Ltd.. 1921. Last Accessed 12/3/2018. Buy the book

Cite this article as:

McAdams, David E. Perpendicular Bisector Concurrence Theorem. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup, updated geogebra app. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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