In triangle ABC, angle C is 90 °, AB = 30, BC = 5 13. Find the radius of the circle around this triangle.

To solve the problem, consider the figure.

Since the circle is described around the right-angled triangle ABC, the center O of this circle is located in the middle of the hypotenuse AB of the right-angled triangle, therefore the radius of the circle is equal to half the length of the hypotenuse AB.

By the Pythagorean theorem, we find the hypotenuse of the triangle.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 30 ^ 2 + (5 * √13) ^ 2 = 900 + 325 = 1225.

AB = √1225 = 35.

Then the radius of the circle AO = AB / 2 = 35/2 = 17.5 cm.

Answer: The radius of the circle is 17.5 cm.