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

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For each interior angle of the triangle below, draw a line that bisects that angle. Move the vertices of the triangle around to see how these bisectors change. What do you notice?

The three bisectors meet at a common point. This point is called the incenter of the triangle. The incenter of a triangle marks the center of an inscribed circle. Project the incenter onto any of the three sides of the triangle. Now draw a circle centered at the incenter and going through this new point. Notice how this circle fits perfectly inside the triangle.