The Expected Area in a Venn Diagram

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 $\lfloor 10000D\rfloor$