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

Since the triangle ABC is rectangular, then by the Pythagorean theorem we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 7 ^ 2 + 24 ^ 2 = 49 + 576 = 625.

AB = 25 cm.

Since a right-angled triangle is inscribed in a circle, the hypotenuse of a triangle is the diameter of a circle circumscribed around it.

Then OA = AB / 2 = 25/2 = 12.5 cm.

Answer: The radius of the circumscribed circle is 12.5 cm.