Random Chord Division

Calculus Level 5

A chord is formed by connecting two points that are randomly and uniformly chosen along the circumference of a unit circle, dividing the circle into two regions.

The expected value of the area of the larger region is \[A\pi + \dfrac{B}{\pi}, \] where \(A\) and \(B\) are rational numbers. What is \(A+B?\)

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