Let $P, A, B, C$ be points on circle $O$ such that $C$ does not lie on arc $\widehat{BAP}$, $\overline{P A} = 21, \overline{P B} = 56, \overline{P C} = 35$ and $m \angle BP C = 60^\circ$. Now choose point $D$ on the circle such that $C$ does not lie on arc $\widehat{BDP}$ and $\overline{BD} = 39$. What is $AD$?


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