$18 \cdot 107$ Line $H K$ and $B C$ are in the same plane, $M$ is the midpoint of segment $B C$, $B H$ and $C K$ are perpendicular to $H K$. Then
(A) $M H=M K$.
(B) $M H>B K$.
(C) Sometimes $M H=M K$.
(D) $M H>M B$.
(E) $B H<B C$.
(21st American High School Mathematics Examination, 1970)
[Solution] Draw $M N \perp H K$ at $N$,
$\because \quad M$ is the midpoint of $B C$, and $B H \perp H K, C K \perp H K$,
$\therefore \quad M N / / B H / / C K$.
and $N$ bisects $H K$. Therefore, $M N$ is the perpendicular bisector of $H K$.
$$
\therefore M H=M K \text {. }
$$

Hence, the answer is $(A)$.