A right-angled triangle is inscribed in a circle. The legs are 7 and 24 cm Find the S of the circle and the length of the circle.

Since triangle ABC is rectangular, the inscribed angle ABC = 90 and rests on the arc AC, the degree measure of which is 2 * 90 = 180, then the hypotenuse of AC is equal to the diameter of the circumscribed circle.

By the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AB ^ 2 + BC ^ 2 = 49 + 576 = 625.

AC = 25 cm.

Then R = AO = AC / 2 = 25/2 = 12.5 cm.

Determine the area of the circle.

S = π * R ^ 2 = 156.25 * π cm2.

Determine the length of the circle.

С = 2 * π * R = 2 * π * 12.5 = 25 * π cm.

Answer: The area is 156.25 * π cm2, the circumference is 25 * π cm.