$1 \cdot 24$ Given $\frac{y+z}{x}=\frac{z+x}{y}=\frac{x+y}{z}=k$, then the value of $k$ is
(A) 2 or -1.
(B) 2.
(C) -1.
(D) 2 or 1.
(Anhui Province, Anqing and other counties and cities junior high school mathematics competition, 1991)
［Solution］From the given and the property of proportional division, we have
$$
\begin{array}{c}
\frac{(y+z)+(z+x)+(x+y)}{x+y+z}=k, \\
\frac{2(x+y+z)}{x+y+z}=k .
\end{array}
$$

If $x+y+z \neq 0$, then $k=2$;
If $x+y+z=0$, substituting $y+z=-x$ into $\frac{y+z}{x}=k$, we get $k=-1$. Therefore, $k=2$ or -1.
Hence, the answer is $(A)$.