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Ludwik · Answer 1 · 2020-01-09T12:24:54+0000

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
$\sqrt3$ , so that AB has length
$(\sqrt3)^2=3$ .

So the circle has diameter 3, or radius 3/2, and its area is
$\left(\frac32\right)^2\pi=\boxed{\frac{9\pi}4}$ and the answer would be C.

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