Circumradius of Triangle

Triangle ABC has sides of lengths 7, 24, and 25. The triangle is inscribed in a circle, and we want to determine the radius of this circle.

To find the radius $R$ of the circumscribed circle (circumcircle) of the triangle, we can use the formula:

$$R = \f\frac{abc}{4K}$$

where $a$, $b$, and $c$ are the lengths of the sides of the triangle, and $K$ is the area of the triangle.

First, calculate the area $K$ of triangle ABC using Heron's formula, which is:

$$K = \sqrt{s(s-a)(s-b)(s-c)}$$

where $s$ is the semi-perimeter of the triangle.

Calculate $s$ first:

$$s = \f\frac{a + b + c}{2}$$