[ List pairs of similar triangles

Point $D$ lies on side $B C$ of triangle $A B C$, and point $O$ is located on segment $A D$, such that $A O: O D=9: 4$. The line passing through vertex $B$ and point $O$ intersects side $A C$ at point $E$, and $B O: O E=5: 6$. Find the ratio in which point $E$ divides side $A C$.

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