The circumcenter is the center of which circle?

Prepare for the Geometry CBE Exam with targeted resources. Access interactive quizzes and detailed explanations to master geometric concepts effectively and excel in your test!

Multiple Choice

The circumcenter is the center of which circle?

The main idea is a triangle has a special circle that goes through all three vertices, and its center is as far from each vertex as from the others. That circle is the circumcircle, and its center is the circumcenter. So the circumcenter is the center of the circumcircle, the circle that passes through all three vertices. It can be found as the intersection of the perpendicular bisectors of the sides, and it’s equidistant from all three vertices. This is different from the incircle, which is centered at the incenter and touches all three sides; the nine-point circle, which passes through midpoints of the sides and feet of the altitudes; and the excircles, which are tangent to one side and the extensions of the other two.

The main idea is a triangle has a special circle that goes through all three vertices, and its center is as far from each vertex as from the others. That circle is the circumcircle, and its center is the circumcenter. So the circumcenter is the center of the circumcircle, the circle that passes through all three vertices. It can be found as the intersection of the perpendicular bisectors of the sides, and it’s equidistant from all three vertices.

This is different from the incircle, which is centered at the incenter and touches all three sides; the nine-point circle, which passes through midpoints of the sides and feet of the altitudes; and the excircles, which are tangent to one side and the extensions of the other two.

More practice questions