Ready, Aim, Fire!

Geometry Level 5

Suppose we have three concentric circles with respective radii \(1, 2\) and \(3.\) Choose one point, uniformly and at random, on each of these circles and form a triangle with these three points as vertices.

Let \(S\) be the expected area of this triangle. Find \(\lfloor 10000S \rfloor\).

Image credit: Wikimedia Dartboard
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