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

In the ABC triangle, it is known that AC = 7, BC = 24, the angle C is 90 °. Find the radius of the circle described around this triangle.

1. Since one of the angles is 90 °, the triangle is rectangular.
2. The legs of the triangle are known. By the Pythagorean theorem, we find the hypotenuse:
c = √ (72 + 242) = √625 = 25 (cm);
3. Find the area of the triangle:
S = a * b / 2;
S = 7 * 24/2 = 84 (cm2);
4. Find the radius of the circle:
R = (a * b * c) / (4 * S);
R = (7 * 24 * 25) / (4 * 84) = 12.5 (cm);
Answer: the radius of the circle described around this triangle is 12.5 cm.