MIC test question, there is a unique small question: If $\frac{a+b}{a-b}=\frac{b+c}{b-c}=\frac{c+a}{c-a}$, then
$$
\begin{aligned}
a+b+c & =\ldots, a^{2}+b^{2}+c^{2}= \\
\frac{1}{a}+\frac{1}{b}+\frac{1}{c} & =\ldots
\end{aligned}
$$
Let $\frac{c+a}{c-a}=k$, then $a=\left(\frac{k+1}{k-1}\right) b$, $b=\left(\frac{k+1}{k-1}\right) c, c=\left(\frac{k+1}{k-1}\right) a$. It follows that $\frac{k+1}{k-1}=-\frac{1}{2} \pm \frac{\sqrt{3}}{2} i$, hence all three answers are zero.