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In a triangle $A B C$, the altitude from $A$ meets the circumcircle again at $T$. Let $O$ be the circumcenter. The lines $O A$ and $O T$ intersect the side $B C$ at $Q$ and $M$, respectively. Prove that
$\frac{S_{A O C}}{S_{C M T}}=\left(\frac{\sin B}{\cos C}\right)^2$
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