9. As shown in Figure 3, in $\triangle A B C$, it is known that $D$ is the midpoint of side $B C$, and $E, F$ are the trisection points of side $A B$. $A D$ intersects $C E, C F$ at points $M, N$ respectively. Then $A M: M N: N D=$ $\qquad$
9. 5:3:2.

As shown in Figure 6, connect $D F$.
Since $D$ is the midpoint of side $B C$, and $E, F$ are the trisection points of side $A B$, we have
$$
\begin{array}{l}
D F \parallel C E \\
\Rightarrow A M=\frac{1}{2} A D .
\end{array}
$$

Draw a line through point $D$ parallel to $A B$, intersecting $C F$ at point $G$. Then
$$
\frac{N D}{A N}=\frac{D G}{A F}=\frac{B F}{2 A F}=\frac{1}{4} \text {. }
$$

Thus, $N D=\frac{1}{5} A D$.
Also, $M N=A D-\frac{1}{2} A D-\frac{1}{5} A D=\frac{3}{10} A D$, so
$$
A M: M N: N D=\frac{1}{2}: \frac{3}{10}: \frac{1}{5}=5: 3: 2 \text {. }
$$