Complex Numbers

Let $\mathrm{C}$ be the circle in the complex plane with centre $\mathrm{z}_{0}=\frac{1}{2}(1+3 i)$ and radius $r=1$. Let $\mathrm{z}_{1}=1+\mathrm{i}$ and the complex number $z_{2}$ be outside the circle $C$ such that $\left|z_{1}-z_{0}\right|\left|z_{2}-z_{0}\right|=1$. If $z_{0}, z_{1}$ and $z_{2}$ are collinear, then the smaller value of $\left|z_{2}\right|^{2}$ is equal to :