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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