In a circle with center \(O\) and radius \(10\), a rectangle \(ABCD\) is inscribed such that \(AB\) and \(CD\) are parallel to the diameter \(EF\) of the circle. Given that the length of \(AB\) is \(16\), find the area of triangle \(AOC\), where \(A\) and \(C\) are vertices of the rectangle and \(O\) is the center of the circle. Let's think step by step and output the final answer within \boxed{}.
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