Radius of the circle circumscribed around a triangle

Radius of the circle circumscribed around the triangle. The radius of the circle circumscribed around a triangle is called the circumradius or the radius of the circumscribed circle. This radius represents the distance from the center of the circle to the vertices of the triangle. The circumscribed circle is also known as the circumscribed circle of the triangle. The circumscribed circle has the property of touching all three sides of the triangle.

The radius of the circumscribed circle can be calculated using the law of sines and the formula:
\[ R = \frac{abc}{4S} \]
where:
R - radius of the circumscribed circle,
a,b,c - lengths of the triangle's sides,
S - area of the triangle.

The radius of the circumscribed circle is an important parameter in triangle geometry and is used in solving various problems related to triangles.