Which center is located at the intersection of the perpendicular bisectors of a triangle?

The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect. This point is significant because it is equidistant from all three vertices of the triangle, which means it serves as the center of the circumcircle, the circle that can be drawn around the triangle that passes through all its vertices.

To find the circumcenter, one can draw the perpendicular bisectors of at least two sides of the triangle. The point where these bisectors meet is the circumcenter. This property is true for all types of triangles, including acute, obtuse, and right triangles, making the circumcenter a fundamental concept in triangle geometry.

In contrast, the incenter is located at the intersection of the angle bisectors, while the centroid is the intersection point of the medians, and the orthocenter is formed by the intersection of the altitudes. Each of these points has its unique properties and roles in triangle geometry, but only the circumcenter specifically relates to the perpendicular bisectors of the triangle's sides.