The Circumcenter

We have already seen that the three perpendicular bisectors of the sides of a triangle meet at a common point which is the center of its circumcircle:

 

 

This is true because points on a perpendicular bisector are equidistant from the endpoints of the segment it bisects, so the intersection of any two perpendicular bisectors of sides of the triangle will be equidistant from the vertices of those sides, and therefore the center of the circumcircle.

The center P of the circumcircle is called the "circumcenter" of the triangle.

toc | return to top | next page