A circle is described around a right-angled triangle with sides of 5 cm, 12 cm and 13 cm. What is the radius of the circle?

Let’s find out what the area of a right-angled triangle will equal, whose legs, according to the condition of the problem, are equal to 5 centimeters and 12 centimeters, when we know that it is calculated as half of their product:

5 * 12 * 1/2 = 30.

Let’s find out what value the radius of the circle will correspond to, which was described around our geometric figure, when in the condition of our problem it is said that the hypotenuse is 13 centimeters:

(5 * 12 * 13) / (4 * 30) = (60 * 13) / (120) = 6.5.

Answer: The radius is 6.5 cm.