13. As shown in Figure 3, in $\triangle A B C$, $A B=1, A C=2$,
$D$ is the midpoint of $B C$, $A E$
bisects $\angle B A C$ and intersects $B C$ at
point $E$, and $D F / / A E$. Find the length of $C F$.
Three, 13. As shown in Figure 8, draw $E H \perp A B$, intersecting $A B$ at point $H$, and $E G \perp A C$, intersecting $A C$ at point $G$. Since $A E$ bisects $\angle B A C$, we have
$$
E H=E G .
$$

Thus, we have $\frac{B E}{C E}=\frac{S_{\triangle A B E}}{S_{\triangle A E C}}=\frac{A B}{A C}=\frac{1}{2}$.
Furthermore, since $D F / / A E$, we get
$$
\begin{array}{l}
\frac{C F}{C A}=\frac{C D}{C E}=\frac{B C}{2 C E}=\frac{B E+E C}{2 C E}=\frac{1}{2}\left(\frac{B E}{C E}+1\right) \\
=\frac{1}{2}\left(\frac{1}{2}+1\right)=\frac{3}{4} .
\end{array}
$$

Therefore, $C F=\frac{3}{4} \times C A=\frac{3}{4} \times 2=\frac{3}{2}$.