Since the length of the arc ACB is 3 times the length of the arc AB, the angle made by the arc ACB must be
three times the angle made by the arc AB. Now, the two arcs together make 360° at the center of the circle.
Hence, the smaller angle, the angle made by the arc AB, must equal one-quarter of the full angle, which is
360°. One-quarter of 360° is 90°. Hence, 
. Hence, triangle AOB is a right triangle, and
applying The Pythagorean Theorem to the triangle yields
OA = OB = radius of circle = OC = 3 (from the figure)
The answer is (E).