Mean distance between two random points on a circle

Choose two points independently and uniformly on the circumference of a circle of radius $1$. The expected length of the segment joining them can be written as $\dfrac{x}{\pi}$ with $x$ rational. What is $x$?

$x=4$. By rotation, fix one point; the central angle $\theta$ to the other is uniform on $[0,2\pi)$ and the chord is $2\sin(\theta/2)$. Averaging, $\tfrac{1}{2\pi}\int_0^{2\pi}2\sin(\theta/2)\,d\theta=\tfrac{8}{2\pi}=\tfrac4\pi$.