5. Based on the base $AC$ of the isosceles triangle $ABC$, a circle is constructed with $AC$ as its diameter, intersecting the side $BC$ at point $N$ such that $BN: NC = 7: 2$. Find the ratio of the lengths of the segments $AN$ and $BC$.
Answer: $\frac{A N}{B C}=\frac{4 \sqrt{2}}{9}$.

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