In triangle ABC, it is known that AC = 7, BC = 24, angle C is 90. find the radius of the circle circumscribed

In triangle ABC, it is known that AC = 7, BC = 24, angle C is 90. find the radius of the circle circumscribed about this triangle.

Given: right-angled triangle ABC;

angle C = 90;

leg AC = 7;

leg BC = 24.

Find: find the radius described around the triangle ABC of the circle, that is, R -?

Decision:

1. Consider a right-angled triangle ABC. By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

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

7 ^ 2 + 24 ^ 2 = AB ^ 2;

49 + 576 = AB ^ 2;

625 = AB ^ 2;

AB = 25.

2. The radius of a circumscribed circle about a right-angled triangle is half the hypotenuse, that is:

R = 1/2 * AB;

R = 1/2 * 25;

R = 12.5.

Answer: 12.5.