A circle is described around a right-angled triangle ABC with a right angle C = 90 degrees.

A circle is described around a right-angled triangle ABC with a right angle C = 90 degrees. Find the radius of this circle if AC = 8cm, Bc = 6cm.

Consider a right-angled triangle ABC.

According to the condition of the problem, the angle is C = 90 °, AC = 8 and BC = 6.

By the Pythagorean theorem, AB ^ 2 = AC ^ 2 + CB ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100,

So AB = 10.

But the hypotenuse of a right-angled triangle is equal to the diameter of the circumscribed circle.

Therefore, the radius of the circle is equal to half of the hypotenuse AB / 2 = 10/2 = 5.

Answer: 5.