In the triangle abc it is known that ac = 33, bc = √355, angle C is 90. Find the radius of the circumscribed circle of this rectangle.

Any right-angled triangle that is inscribed in a circle is built on the diameter of this circle, that is, AB is the hypotenuse of triangle ABC and the diameter of the circumscribed circle.
Find AB by the Pythagorean theorem:
AB = √ (AC ^ 2 + BC ^ 2);
AB = √ (33 ^ 2 + (√355) ^ 2) = √ (1089 + 355) = √1444 = 38 (cm).
The radius of the circumscribed circle is equal to half of its diameter, therefore:
r = AB / 2 = 38/2 = 19 (cm).
Answer: r = 19 cm.