In triangle ABC, it is known that AC = 6, BC = 8, angle C is 90 °. Find the radius of the circle circumscribed about this triangle.

We have a right-angled triangle ABC, with a right angle C, where AC, BC are the legs, AB is the hypotenuse. We also have a circumscribed circle, the radius of which we can find as half of the hypotenuse, first we find the hypotenuse by the Pythagorean theorem:

AB ^ 2 = AC ^ 2 + BC ^ 2;

AB ^ 2 = 6 ^ 2 + 8 ^ 2;

AB ^ 2 = 36 + 64;

AB ^ 2 = 100;

AB = 10 cm.

Since we found the length of the hypotenuse, we can immediately find the radius of the circumscribed circle as:

R = AB / 2;

R = 10/2;

R = 5 cm.

Answer: the radius of the circumscribed circle is 5 cm.