In the right triangle \(ABC\) above, the length of \(AB\) is \(5\sqrt3.\) What is the area of triangle \(ABC?\)

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In the right triangle \(ABC\) above, the length of \(AB\) is \(5\sqrt3.\) What is the area of triangle \(ABC?\)

(1) \(DBC\) is an equilateral triangle.
(2) \(ABD\) is an isosceles triangle.


[spoiler]OA=A[/spoiler]

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