$17 \cdot 68$ In a right triangle with legs $a, b$, and hypotenuse $c$, the altitude to the hypotenuse divides $c$ into segments $r$ and $s$, which are adjacent to $a$ and $b$ respectively. If $a: b=1: 3$, then the ratio of $r$ to $s$ is
(A) $1: 3$.
(B) $1: 9$.
(C) $1: 10$.
(D) $3: 10$.
(E) $1: \sqrt{10}$.
(9th American High School Mathematics Examination, 1958)
［Solution］By the property of similar triangles, we have
$$
a^{2}=r c, \quad b^{2}=s c .
$$

Therefore, $\frac{r}{s}=\frac{r c}{s c}=\frac{a^{2}}{b^{2}}=\left(\frac{a}{b}\right)^{2}=\frac{1}{9}$. Hence, the answer is $(B)$.