3. As shown in Figure 1, points $B, C, D$ are on the same straight line, and $A B=B C=C A, C D=D E=E C, A D$ intersects $B E$ at point $F$. If $B C: C D=1: 2$, then $B F: D F=$ ( ).
(A) $1: 2$
(B) $2: 3$
(C) $3: 4$
(D) None of the above
$$
\begin{aligned}
\triangle A C D \cong \triangle B C E \\
\Rightarrow A D=B E \\
\Rightarrow C G=C H \\
\Rightarrow F C \text { bisects } \angle D F B \\
\Rightarrow B F: D F=B C: C D=1: 2 . \\
\quad \text { 3. A. }
\end{aligned}
$$

As shown in Figure 6, connect $C F$, draw $C G \perp A D$ at point $G$, $C H \perp B E$ at point $H$. Then