Let $C$ and $D$ be points on the circle with center $O$ and diameter $[AB]$, where $C$ and $D$ are on different semicircles with diameter $[AB]$. Let $H$ be the foot of the perpendicular from $B$ to $[CD]$. If $|AO| = 13$, $|AC| = 24$, and $|HD| = 12$, what is $\widehat{DCB}$ in degrees? If the answer is $x^\circ$, what is the value of $x$?

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