by Amy Benson

Circumcenter of A Triangle

The circumcenter of a triangle is located at the intersection of the perpendicular bisectors of the sides of the triangle.

It is interesting to examine the location of the circumcenter for different classifications of triangles.

Acute Triangles

Acute Isosceles

In this instance, the circumcenter is located in the interior of the triangle.

Acute Scalene

Again, the circumcenter is located in the interior of the given triangle.

Acute Equilateral

In this final classification of acute triangles, we again find that the circumcenter is inside the triangle.

CONCLUSION: The circumcenter of any acute triangle is located in the interior of the triangle.

Right Triangles

Right Isosceles

In this instance, we see that the circumcenter is located at the midpoint of the hypotenuse of the triangle. To test that this is true for any right isosceles triangle, click here.

Right Scalene

Again, we find that the circumcenter is located at the midpoint of the hypotenuse.

CONCLUSION: The circumcenter of a right triangle is located at the midpoint of the hypotenuse.

Obtuse Triangles

Obtuse Scalene

In this case, we see that the circumcenter is located outside of the given triangle. Also, notice that is opposite the obtuse angle. To try this for yourself, click here.

Obtuse Isosceles

We find the same situation in this instance. The circumcenter is outside the triangle, opposite the obtuse angle. To explore, click here.

CONCLUSION: The circumcenter of an obtuse triangle is located outside the triangle, opposite the obtuse angle.