CEMC Pascal, 2007

Geometry Difficulty 3.0 AMC 10/12 Find the answer Canada

In the diagram, two circles, each with centre $D$ , have radii of $1$ and $2$ . The total area of the shaded regions is $\frac{5}{12}$ of the area of the larger circle. What is a possible measure of $\angle ADC$ ?

(A) $108^\circ$ (B) $120^\circ$ (C) $90^\circ$ (D) $150^\circ$ (E) $135^\circ$

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