Let $z_1=10+6i$ and $z_2=4+6i$. If $z$ be a complex number such that $\text{arg}\left( \frac{z-z_1}{z-z_2} \right)=\frac{\pi}{4}$, then find the value of $|z-7-9i|$. Give your answer up to 3 decimal places.

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