# Yay for 2014! #7

Geometry Level 4

Let $$ABDC$$ be a rectangle, as shown above, such that $$AB = 20$$ and $$AC = 14.$$ Points $$E$$ and $$F$$ are located in the interior of $$ABDC$$ such that the triangles $$AEC$$ and $$BFD$$ are equilateral. The area of the intersection of these triangles can be represented by

$\frac{a\sqrt{3}}{b}- c,$

where $$a, b,$$ and $$c$$ are positive integers with $$\gcd(a, b) = 1.$$ Find $$a+b+c.$$

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