Which term describes the circle that passes through all three vertices of a triangle?

• A. Circumcircle
• B. Orthocenter
• C. Centroid
• D. Incircle

Answer: (A)

A circle that passes through all three vertices is called the circumcircle. For any non-degenerate triangle, there is a unique circle that goes through its three corners. The center of this circle, the circumcenter, lies where the perpendicular bisectors of the sides meet, and it is the same distance from each vertex. That common distance is the circle’s radius, so every vertex lies on the circle.

This circle is different from the incircle, which is tangent to all three sides; and different from the orthocenter or the centroid, which are specific points associated with altitudes and medians, respectively. The key idea is that the circumcircle is the circle through the triangle’s vertices.