Circumscribed Circle

Definition

A circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter, and its radius is called the circumradius.

Description

In geometry, the concept of a circumscribed circle is significant because it provides a unique way to relate the vertices of a polygon through a single circle. This relationship is particularly useful in various geometric constructions and proofs. For example, every triangle has a unique circumcircle, which can be constructed by finding the intersection of the perpendicular bisectors of the triangle's sides. This circumcircle is essential in triangle geometry as it helps in locating the circumcenter, which is equidistant from all three vertices of the triangle.

The circumcircle's properties extend to other polygons as well, such as regular polygons, rectangles, and certain types of quadrilaterals like isosceles trapezoids and right kites. However, not all polygons have a circumcircle; only cyclic polygons do. Understanding the circumcircle is crucial for solving problems related to cyclic polygons, optimizing geometric shapes, and in various applications like navigation and engineering.

For a complete collection of terms related to polygons click on this link: Polygons Collection.