In parallelogram $ABCD$, angles $B$ and $D$ are acute while angles $A$ and $C$ are obtuse. The perpendicular from $C$ to $AB$ and the perpendicular from $A$ to $BC$ intersect at a point $P$ inside the parallelogram. If $PB = 700$ and $PD = 821$, what is $AC$?

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