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 of the circumscribed circle ABC, 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.