Is the diagonal of the rectangle inscribed in a circle always the diameter of the circle??

I was solving the below question:

http://gmatclub.com/forum/rectangle-abcd-is-inscribed-in-a-circle-as-shown-above-what-15182.html#p1116066Rectangle ABCD is inscribed in a circle as shown above. What is the radius of the circle?

(1) The length of the rectangle is sqrt(3) and the width of the rectangle is 1.

(2) The length of arc AB is 1/3 of the circumference of the circle.

I got C as an answer assuming that the diagonal need not be the diameter. Please clarify whether the diagonal of the rectangle inscribed in a circle always the diameter of the circle??