Triangle ADE is equilateral so each of its interior angles haves measure 60 degrees. AB is a diameter of the circle because it passes through C. Then AB is perpendicular to ED, which means triangle ABD is a 30-60-90 triangle.
In this triangle, the lengths of BD, AD, and AB occur in a ratio of 1 to 2 to [tex]\sqrt3[/tex], so that AB has length [tex](\sqrt3)^2=3[/tex].
So the circle has diameter 3, or radius 3/2, and its area is [tex]\left(\dfrac32\right)^2\pi=\boxed{\dfrac{9\pi}4}[/tex] and the answer would be C.
