Pick two points A and B at random independently from the circumference of the unit circle by choosing two angles independently and uniformly from $[0, 2 \pi)$ and choosing two points with corresponding angles in the polar representation.
If $D$ is the perpendicular distance of AB from the origin and $\Theta$ is the angle A B makes with the x-axis, what is the density of $D, \Theta$ ?
I am facing difficulty as quite a lot of cases are coming up depending on the positions of the points$A,B$ .