What is the point of concurrency of the perpendicular bisectors of the sides of a triangle called?

The point of concurrency of the perpendicular bisectors of the sides of a triangle is known as the circumcenter. This point has the unique property that it is equidistant from all three vertices of the triangle, meaning that it can serve as the center of a circle that passes through each vertex, known as the circumcircle.

To locate the circumcenter, one would construct the perpendicular bisectors of each side of the triangle. The point where all three bisectors intersect is the circumcenter. This geometrical characteristic is particularly useful in various applications, such as in constructing circumcircles and solving problems related to triangle geometry and distance.

In contrast, other points of concurrency, such as the incenter, centroid, and orthocenter, have different definitions and properties pertaining to the angles and areas of the triangle, rather than being concerned with the distance from the vertices.