In the diagram above, \(A\) is the center of the circle, angle \(BAD = 90^{\circ},\) and the area of triangle \(ABD\) is

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In the diagram above, \(A\) is the center of the circle, angle \(BAD = 90^{\circ},\) and the area of triangle \(ABD\) is \(24\sqrt3.\) What is the area of the circle?

(1) \(AB = 12\)

(2) \(AD = CD\)

Answer: D