In triangle ABC, angle C is 90, AC = 8, BC = 15. Find the radius of the circumscribed circle of this triangle.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 8 ^ 2 + 15 ^ 2 = 64 + 225 = 289.

AB = 17 cm.

Since the circle is described around a right-angled triangle, the degree measure of the arc AB is equal to two values of the angle ACB, then the arc AB = 2 * 90 = 180, and then the hypotenuse AB is the diameter of the circumscribed circle.

Then R = ОВ = AB / 2 = 17/2 = 8.5 cm

Answer: The radius of the circumscribed circle is 8.5 cm.