$P$ is the intersection point of diagonals of cyclic quadrilateral $ABCD$. The circumcenters of $\triangle APB$ and $\triangle CPD$ lie on the circumcircle of $ABCD$. If $AC + BD = 18$, find the area of $ABCD$. The original answer is in the form \(\frac{k\sqrt{m}}{n}\), please give the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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