In triangle ABC, angle C is 90 degrees, AB = 3, BC = 4. Find the radius of the circumscribed circle of this triangle

Since the angle C is 90 °, the triangle is right-angled. We find its hypotenuse using the Pythagorean theorem, we get:

AC ^ 2 = AB ^ 2 + BC ^ 2 = 3 ^ 2 + 4 ^ 2 = 25;

AC = 5.

In a right-angled triangle, the radius of the circumscribed circle is 1/2 of its hypotenuse:

R = AC / 2 = 5/2 = 2.5.

Answer: the required radius is 2.5.