Circumcenter of a Triangle

Topic:Circle, Circumcircle or Circumscribed Circle, Triangles

In this activity, you will explore the circumcenter of a triangle. Each side of the triangle below has a perpendicular bisector. Drag points A, B, and C to uncover patterns about the perpendicular bisectors of different types of triangles.

What do you notice about the intersection of the perpendicular bisectors? Is this always true? Drag the vertices of the triangle to see what happens to the intersection as the triangle changes.

All three perpendicular bisectors will always intersect at the same point. This point is called the circumcenter.

The applet above contains the same triangle with perpendicular bisectors as the first applet. The circumcenter is labelled point G. Then, we drew a circle centered at G that extends to point A. What do you notice about the other vertices of the triangle?

Circumcenter of a Triangle

What do you notice about the intersection of the perpendicular bisectors? Is this always true? Drag the vertices of the triangle to see what happens to the intersection as the triangle changes.

All three perpendicular bisectors will always intersect at the same point. This point is called the circumcenter.

The applet above contains the same triangle with perpendicular bisectors as the first applet. The circumcenter is labelled point G. Then, we drew a circle centered at G that extends to point A. What do you notice about the other vertices of the triangle?

Write a 1-3 sentence summary of what you learned about the circumcenter of a triangle.

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