Create 3. In the right-angled triangle $\triangle A B C$, $A D$ is the median on the right side $B C$, $B E \perp A D$ at $G$, and intersects $A C$ at $E, E F \perp B C$ at $F$. Given $A B=B C=a$, find the length of $E F$.
(A) $\frac{1}{3} a$
(E) $\frac{1}{2} a$
(C) $\frac{2}{3} a$
(D) $\frac{2}{5} a$
Analysis: From the right triangle $\mathrm{Rt} \triangle A B C$ and the median $A D \perp B E$, we can derive that $A G \cdot G D=4 \cdot 1$. Since $D$ is the midpoint of $B C$, and $\triangle A B C$ is the original triangle, from (*) we have $(1+1) \cdot \frac{A E}{E C}=4$, so $\frac{A E}{E C}=2$. Therefore, $\frac{E C}{A C}=\frac{1}{3}$.
Since $\triangle E F C \sim \triangle A B C$, then $E F: A B=E C: A C=\frac{1}{3}$. Hence, the answer is (A).