\textbf{11.} Triangle $ABC$ has sides $\sqrt{3}$, $6$, and $\alpha$ (with the angle between them being $\alpha$) and is inscribable in a circle. If the area of this triangle is at most $4.5$, what is the minimum value of $\alpha$?
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(1) $2$ \hfill (2) $3$ \hfill (3) $4$ \hfill (4) $5$
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