The Expected Area in a Venn Diagram

Calculus Level 5

Consider the two circles of equal radius \(2\) units, intersecting, with the common chord \(BC\) that subtends an angle \(120\) degrees at the centre of either circle. Let \(A\) be a point that is uniformly distributed on the major arc of \(BC\). If the expected area of \(\triangle ABC\) is \(D\), find \(\lfloor 10000D\rfloor\)

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