18・112 In trapezoid $A B C D$, $A B / / C D, A B=3 C D, E$ is the midpoint of diagonal $A C$, and line $B E$ intersects $A D$ at $F$. Then the value of $A F: F D$ is
(A)2.
(B) $\frac{5}{3}$.
(C) $\frac{3}{2}$.
(D) 1 .
(Huanggang Region, Hubei Province, China Junior High School Mathematics Competition, 1996)
[Solution] Draw $C G / / B F$ intersecting the extension of $A D$ at $G$ (as shown in the figure).
From $A B / / C D, C G / / B F$ we get $\triangle A B F \backsim \triangle D C G$,
thus $A F: D G=A B: D C=3: 1$.
Furthermore, since $C G / / B F, A E=E C$, we have $A F=$
$F G$,
therefore
$$
F D=2 D G
$$

Hence $A F: F D=3: 2=\frac{3}{2}$.
Therefore, the answer is $(C)$.