The point of concurrency of the three perpendicular bisectors, equidistant from each vertex of the triangle and the centre of the circumcircle is called what?

• A. Incenter
• B. Circumcenter
• C. Centroid
• D. Orthocenter

Answer: (B)

The main idea is the circumcenter—the point where the perpendicular bisectors of the triangle’s sides meet. A perpendicular bisector of a side is the set of all points that are equidistant from the two endpoints of that side. If a single point lies on all three perpendicular bisectors, it is equidistant from all three vertices, so it serves as the center of a circle that passes through all three vertices—the circumcircle. That common intersection is therefore the circumcenter. In different triangles this center can lie inside, on, or outside the triangle depending on the type of triangle. For contrast, the incenter is equidistant from the sides, the centroid is the balance point along the medians, and the orthocenter is where the altitudes meet; none of these are the intersection of the perpendicular bisectors or the center of the circumcircle.