CIRCUMCENTER AND ITS CIRCLE

BY

CAROLYN JOHNSON

UNIVERSITY OF GEORGIA

The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of each side of the triangle. Usually labeled C, the circumcenter lies on the point of intersection of all three perpendicular bisectors of the triangle. The circumcenter is the point in the triangular plane that is equidistant from each of the triangle's vertices. This equal distance from the circumcenter to each of the vertices becomes the radius of the circumcircle, the circle that passes through all three vertices.

Looking at our graph we see the circumcenter is located inside the triangle. Does it always stay within the triangle? I would guess that it would not always stay inside the triangle. Let's see if I'm right or not.

When the triangle is a right triangle the circumcenter is located at the midpoint of one of the sides of the triangle. Let's look at an obtuse triangle and see what happens.

So we see that in an obtuse triangle the circumcenter is located outside the triangle. This is similar to the locations of the orthocenter of a triangle. Let's compare the graphs side by side to see the different locations of the circumcenter.

Now let's look at the circles that are formed with the different locations of the circumcenters. Remember that the circumcenter is the center of the circle that passes through all three vertices of the triangle.

The circles created by the circumcenters are called "circumcircles."