17-69 In a right triangle, the two legs are $a, b$, and the hypotenuse is $c$, the altitude to the hypotenuse is $x$, then
(A) $a b=x^{2}$.
(B) $\frac{1}{a}+\frac{1}{b}=\frac{1}{x}$.
(C) $a^{2}+b^{2}=2 x^{2}$.
(D) $\frac{1}{x^{2}}=\frac{1}{a^{2}}+\frac{1}{b^{2}}$.
(E) $\frac{1}{x}=\frac{b}{a}$.
(7th American High School Mathematics Examination, 1956)
[Solution] Given $2 S_{\triangle}=a b=c x$, thus $a^{2} b^{2}=c^{2} x^{2}$. That is, $a^{2} b^{2}=\left(a^{2}+b^{2}\right) x^{2}$, hence $\frac{a^{2}+b^{2}}{a^{2} b^{2}}=\frac{1}{x^{2}}$. Therefore, the correct choice is $(D)$.