In triangle ABC, it is known that AC-8 BC = 15 and the angle C is 90 degrees.

In triangle ABC, it is known that AC-8 BC = 15 and the angle C is 90 degrees. Find the radius of the circumscribed circle around this triangle?

In triangle ABC it is known:

AC = 8;
BC = 15;
Angle C = 90 °.
Find the radius of the circle circumscribed about this triangle.

1) The radius of the circumscribed circle of a right-angled triangle is half the hypotenuse.

2) Find the hypotenuse AB of the triangle ABC by the Pythagorean theorem.

AB = √ (AC ^ 2 + BC ^ 2) = √ (8 ^ 2 + 15 ^ 2) = √ (64 + 225) = √289 = √17 ^ 2 = 17;

3) Find the radius.

R = 1/2 * AB = 1/2 * 17 = 17/2 = 8.5;

This means that the radius of the circumscribed circle of a right-angled triangle is 8.5.

Answer: R = 8.5.