8. Let the three vertices of $\triangle A B C$ in the complex plane correspond to the complex numbers $z_{1}, z_{2}, z_{3}$, and $\left|z_{1}\right|=r(r>0$ is a constant), $z_{2}=\overline{z_{1}}, z_{3}=\frac{1}{z_{1}}$, find the maximum value of the area of $\triangle A B C$.
8. Let $z_{1}=r(\cos \theta+i \sin \theta)$, so $S_{\triangle A B C}=\left(1-\frac{1}{r^{2}}\right) S_{\triangle O z_{1} z_{2}}=$ $\left(1-\frac{1}{r^{2}}\right) r^{2}|\cos \theta \sin \theta|=\left(r^{2}-1\right)|\cos \theta \sin \theta| \leqslant \frac{1}{2}\left(r^{2}-1\right)$, equality holds when $\theta=\frac{\pi}{4}$.