In triangle ABC, it is known that AC = 12, BC = 5, the angle is 90 degrees. Find the radius of the circle

In triangle ABC, it is known that AC = 12, BC = 5, the angle is 90 degrees. Find the radius of the circle circumscribed about this triangle.

Since, by condition, triangle ABC is rectangular and it is inscribed in a circle, its hypotenuse coincides with the diameter of the circle, and the center of circle O is the midpoint of the hypotenuse.

ОА = ОВ = AB / 2 = R.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 12 ^ 2 + 5 ^ 2 = 144 + 25 = 169.

AB = 13 cm.

Then OA = R = 13/2 = 6.5 cm.

Answer: The radius of the circle is 6.5 cm.