{"status": "success", "data": {"description_md": "Regular hexagon $ABCDEF$ with side length $1$ is inscribed in a rectangle $WXYZ$, such that $A$ lies on size $WX$, $C$ lies on side $XY$, $D$ lies on side $YZ$, and $F$ lies on side $WZ$. As well, $E$ and $B$ lie in the interior of $WXYZ$. Given that the area of rectangle $WXYZ$ is $\\sqrt 3 + \\frac{48}{25}$, the sum of all possible values of the area of triangle $ABX$ can be written as $\\frac{a-b\\sqrt c}{d}$, where $a$, $b$, $c$, and $d$ are positive integers such that $c$ is not divisible by the square of any prime and $\\gcd(a,b,d)=1$. Find $a+b+c+d$.", "description_html": "

Regular hexagon ABCDEF with side length 1 is inscribed in a rectangle WXYZ, such that A lies on size WX, C lies on side XY, D lies on side YZ, and F lies on side WZ. As well, E and B lie in the interior of WXYZ. Given that the area of rectangle WXYZ is \\sqrt 3 + \\frac{48}{25}, the sum of all possible values of the area of triangle ABX can be written as \\frac{a-b\\sqrt c}{d}, where a, b, c, and d are positive integers such that c is not divisible by the square of any prime and \\gcd(a,b,d)=1. Find a+b+c+d.

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