MathNet 2013 Question 86

Let $ABCD$ be a convex quadrilateral. Extend line $CD$ past $D$ to meet line $AB$ at $P$ and extend line $CB$ past $B$ to meet line $AD$ at $Q$. Suppose that line $AC$ bisects $\angle BAD$. If $AD=\frac{7}{4}$, $AP=\frac{21}{2}$, and $AB=\frac{14}{11}$, compute $AQ$.

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