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?
Side length of the square = [ product of the legs / [ sum of the legs ] = (1*1) / ( 1 + 1) = 1/2
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