Brian is standing at a point \(A\) on the circumference of a perfectly circular forest that has an area of \(6400\pi\) sq mi. Using his all knowing brain, he walks in a perfectly straight line towards his friends, camping at point \(B\) chosen uniformly and at random (and independently of \(A\) somewhere along the circumference of the woods. If the expected distance he travels to reach his friends can be represented as \(\frac{a}{\pi}\), find a (in miles).

This problem was inspired by a slight misinterpretation of my other previously ambiguous problem.

This is part of the set Trevor's Ten

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