A circumscribed triangle, also known as a circumtriangle, is a triangle that is inscribed in a circle, meaning all its vertices touch the circle. This circle is called the circumcircle, and its center is known as the circumcenter. The circumcenter is the point where the perpendicular bisectors of the triangle's sides intersect. In a circumscribed triangle, the radius of the circumcircle is called the circumradius. The properties of circumscribed triangles are important in geometry, as they help in understanding relationships between angles and sides. The concept is often used in various mathematical applications, including trigonometry and triangle congruence.