# More Wrecked Angles

Geometry Level 3

In the diagram above, ABCD and PQRS are both rectangles. Points P, Q, R, and S lie on segments $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, and $\overline{DA}$, respectively, and $\overline{BQ} < \overline{QC}$.

If $AB=36$ and $BC=50$, then the maximum possible value of $BQ$ can be written in the form $a-\sqrt{b}$, where $a,b \in \mathbb{N}$. What is $a+b$?

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