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Points $X$, $Y$, and $Z$ are on the sides $\overline{QR}$, $\overline{PR}$, and $\overline{PQ}$, respectively, of right triangle $PQR$ such that $PZXY$ is a square.  If $PQ = 1$ and $PR = 1$, then what is the side length of the square?

 
 Nov 22, 2023

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