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 :