# Of circles, tangents, and triangles?

Geometry Level 5

In the figure above, circle $$B$$ is tangential to circle $$A$$ at $$G$$. $$\overline {AG}$$ is perpendicular to $$\overline {CD}$$, intersecting at $$B$$. The length of $$\overline {CD}$$ is three times the diameter of circle $$B$$. Radii $$AF$$ and $$AE$$ are drawn such that they are tangential to circle $$B$$. If $$\angle FAE$$ can be expressed in the form of $$\cos^{-1} ( \frac{a}{b} )$$ where $$a$$ and $$b$$ are coprime positive integers,

determine $$a \times b$$.

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