$17 \cdot 80$ A women's barracks is located 300 meters from a certain straight road, and a men's barracks is located on this straight road but 500 meters from the women's barracks. Now it is desired to build a restaurant on this straight road, equidistant from each barracks. Then this distance should be
(A) 400 meters.
(B) 250 meters.
(C) 87.5 meters.
(D) 200 meters.
(E) None of the above.
(4th American High School Mathematics Examination, 1953)
[Solution] As shown in the figure, let $G$ be the girls' dormitory, $B$ be the boys' dormitory; and let the canteen be built at point $C$, with $B C = G C = x$.
$$
\begin{aligned}
\because \quad O B & =\sqrt{500^{2}-300^{2}}=400, \\
\therefore \quad G C & =\sqrt{O C^{2}+O G^{2}}, \\
x & =\sqrt{(400-x)^{2}+300^{2}},
\end{aligned}
$$

Thus,
Solving for $x$ gives $x=312.5(\mathrm{~m})$.
Therefore, the answer is $(E)$.