In a right-angled triangle, the legs are 9 and 12 cm. Find the radius of the circumscribed circle.

The radius of the circumscribed circle for a right-angled triangle is calculated by the formula R = c / 2. Where c is the hypotenuse of a right-angled triangle. Using the Pythagorean theorem (Theorem: in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs), we find
c ^ 2 = 9 ^ 2 + 12 ^ 2; here c, 9 and 12 to the second power
c ^ 2 = 81 + 144; here c in the second power
c ^ 2 = 225; here c in the second power
c = 15.
We use the formula R = s / 2
R = 15/2 = 7.5 (cm).