The circumradius is the radius of the circumcircle, which is the circle that passes through all the vertices of a polygon, particularly a triangle. For any triangle, the circumradius can be calculated using the formula R = \fracabc4A , where a , b , and c are the lengths of the triangle's sides, and A is the area of the triangle. In geometry, the circumradius is an important concept because it helps in understanding the relationships between the triangle's sides and angles. The circumcircle is also significant in various applications, including trigonometry and triangle geometry.