Constructing a Circumcenter Chapter 5.1

Perpendicular Bisectors A segment that intersects a segment at its midpoint and is also perpendicular to the segment.

Concurrency When three or more lines intersect at a common point, the lines are called concurrent lines. The point where concurrent lines intersect is called the point of concurrency. The perpendicular bisectors of each side of a triangle are concurrent lines. We call the point of concurrency the circumcenter of the triangle.

Constructing a Circumcenter Construct a perpendicular bisector for each side of the triangle. http://www.mathopenref.com/constbisectline.html Label the point where the three perpendicular bisectors intersect.

3 types of circumcenters Acute Right Obtuse

Circumcenter theorem The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle. Example: If G is the circumcenter of ΔABC, then GB = GA = GC.