circle line picking

Circle line picking is the activity of choosing two points on the circumference a unit circle and calculating probabilities and averages about the chord formed by connecting those two points.

The length of the line segment between the two points is $\sqrt{2-2\cos \theta }$, where $\theta$ is the angle of the central vertex of a triangle formed by connecting the two points to the center. On average, this works out to $\frac{4}{\pi }$.