# 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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