17.54 As shown in the figure, $A B / / E F / / C D$. It is known that $A B=20, C D=80, B C=100$, then the value of $E F$ is
(A) 10.
(B) 12.
(C) 16.
(D) 18.
(China Junior High School Mathematics League, 1991)
[Solution] From the given and the intercept theorem, we have
$$
\begin{array}{l}
\frac{E F}{80}=\frac{B F}{100}, \\
\frac{E F}{20}=\frac{F C}{100},
\end{array}
$$
(1) + (2) gives $\quad \frac{E F}{80}+\frac{E F}{20}=\frac{B F+F C}{100}=1$.

So $E F+4 E F=80$. That is, $5 E F=80$. Hence, $E F=16$. Therefore, the answer is $(C)$.