$20 \cdot 73$ In a right triangle with hypotenuse of length $h$, the radius of the inscribed circle is $r$. The ratio of the area of the inscribed circle to the area of the triangle is
(A) $\frac{\pi r}{h+2 r}$.
(B) $\frac{\pi r}{h+r}$.
(C) $\frac{\pi r}{2 h+r}$.
(D) $\frac{\pi r^{2}}{h^{2}+r^{2}}$.
(E) None of these.
(30th American High School Mathematics Examination, 1979)
[Solution] As shown in the figure, let $x$ and $y$ be the lengths of the legs of the right triangle, so

that is
$$
h=(y-r)+(x-r)=x+y-2 r \text {, }
$$

Also, $x^{2}+y^{2}=h^{2}$, then
$$
\begin{aligned}
S_{\triangle A B C} & =\frac{1}{2} x y \\
& =\frac{1}{2}\left[\frac{(x+y)^{2}-\left(x^{2}+y^{2}\right)}{2}\right] \\
& =\frac{1}{4}\left[(h+2 r)^{2}-h^{2}\right] \\
& =h r+r^{2} .
\end{aligned}
$$

Thus, the required ratio is $\frac{\pi r^{2}}{h r+r^{2}}=\frac{\pi r}{h+r}$. Therefore, the answer is $(B)$.