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In $\triangle PQR$, we have $\angle P = 30^\circ$, $\angle Q = 60^\circ$, and $\angle R = 90^\circ$. Point X is on $\overline{PR}$ such that $\overline{QX}$ bisects $\angle PQR$. If PQ=12, then the area of is $\mathcal A$. What is $\mathcal A^2$?