Triangle $ACE$ is equilateral with side lengths of $8.$ Points $B$ and $D$ are the midpoints of line segments

Triangle $ACE$ is equilateral with side lengths of $8.$ Points $B$ and $D$ are the midpoints of line segments $AC$ and $CE$ respectively. Line segment $BD$ is a diameter of the circle with center $F.$ What is the area of the shaded region?

A. $8\sqrt2 - 4\pi$
B. $12\sqrt3-2\pi$
C. $12\sqrt3 - 4\pi$
D. $16\sqrt3 - 2\pi$
E. $16\sqrt2 - 4\pi$

Answer: B

Source: Princeton Review

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