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

1. Since the angle C is equal to 90 °, we conclude that the triangle is rectangular.
2. Both legs are known. Since the lengths of the legs AC and BC are respectively 3 cm and 4 cm, this triangle is Egyptian, which means that the hypotenuse AB is 5 cm.
3. Find the area of the triangle:
S = a * b / 2 = 3 * 4/2 = 6 (cm2);
4. Find the radius of the circumscribed circle:
R = (a * b * c) / (4 * S);
R = (3 * 4 * 5) / (4 * 6) = 2.5 (cm);
Answer: the radius of the circumscribed circle is 2.5 cm.