O is the center of a semicircle, ABCD is a rectangle.
A, O and B are collinear.
$|AE| = |ED| = \dfrac{1}{2}$ unit, $m(\widehat{AOE}) = x$
Points C and D lie on the semicircle with center O.
What is the length of a diagonal of rectangle ABCD in terms of $x$?
A) $\tan x$
B) $\operatorname{cosec} x$
C) $\sec x$
D) $\sin x$
E) $\cos x$