Question

Which statement correctly describes the location of the circumcenter of a triangle?

A) The circumcenter is on the inside of an obtuse triangle.

B) The circumcenter is on one of the vertices of an acute triangle.

C) The circumcenter is on the outside of an obtuse triangle.

D) The circumcenter is on one of the sides of an acute triangle.

Answer 1

C) The circumcenter is on the outside of an obtuse triangle.

Explanation:

You want to know where the circumcenter is in relation to the sides and vertices of different triangles.

Circumcenter

The circumcenter of a triangle is the center of the circle through its vertices. As such, it will never lie on a vertex of the triangle.

As you can see in the attached figure, the circumcenter of an acute triangle is inside the triangle.

For a right triangle, the circumcenter is the midpoint of the hypotenuse.

The circumcenter of an obtuse triangle is outside the triangle.

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Additional comment

The circumcenter is located at the point where the perpendicular bisectors of the sides meet.

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