Around a right-angled triangle, a circle with a radius of 8.5 cm is described.

Around a right-angled triangle, a circle with a radius of 8.5 cm is described. What is the area of this triangle if the length of one of its legs is 8 cm.

A right angle inscribed in a circle is always based on the diameter. This means that the hypotenuse of this triangle is equal to the diameter of the circle: 8.5 * 2 = 17 cm. Knowing the length of the hypotenuse and one of the legs, we can find the second leg: 17 ^ 2-8 ^ 2 = 289-64 = 225. The length of the second leg is equal to the root of 225: √225 = 15 cm. The area of the triangle is found as half of the product of the legs: S = 0.5 * 15 * 8 = 60 cm2.