CEMC Pascal, 2002

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, $ABC$ is a semi-circle with diameter $AC$ , centre $O$ and radius 1. Also, $OB$ is perpendicular to $AC$ . Using $AB$ as a diameter, a second semi-circle $AEB$ is drawn. The region inside this second semi-circle that lies outside the original semi-circle is shaded, as shown. The area of this shaded region is

(A) $\dfrac{\pi}{4}$ (B) $\dfrac{1}{2}$ (C) $\dfrac{3\pi}{4}+\dfrac{1}{2}$ (D) $\dfrac{3}{4}$ (E) $\dfrac{\pi}{2}-\dfrac{1}{2}$

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