David Little
Mathematics Department
Penn State University
Eberly College of Science
University Park, PA 16802
Office: 403 McAllister
Phone: (814) 865-3329
Fax: (814) 865-3735
e-mail:dlittle@psu.edu

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Circumcenter
The perpendicular bisector of a line segment L with endpoints A and B is the line perpendicular to L that passes through the midpoint of A and B. For each edge of the triangle below, draw it's perpendicular bisector.

Move the vertices of the triangle around to see how the perpendicular bisectors change. What do you notice?

Like the medians of a triangle, the three perpendicular bisectors have a single point in common. This point is called the circumcenter. The circumcenter of a triangle marks the center of a circle which contains the vertices of the triangle.

Draw a circle centered at the circumcenter that passes through one of the vertices. Notice that this circle also passes through the other two vertices of the triangle.