Complex Numbers

Consider the following two statements :

Statement I: For any two non-zero complex numbers \(z_1, z_2,(|z_1|+|z_2|)\left|\frac{z_1}{\left|z_1\right|}+\frac{z_2}{\left|z_2\right|}\right| \leq 2\left(\left|z_1\right|+\left|z_2\right|\right) \text {, and }\)

Statement II : If \(x, y, z\) are three distinct complex numbers and \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) are three positive real numbers such that \(\frac{\mathrm{a}}{|y-z|}=\frac{\mathrm{b}}{|z-x|}=\frac{\mathrm{c}}{|x-y|}\), then \(\frac{\mathrm{a}^2}{y-z}+\frac{\mathrm{b}^2}{z-x}+\frac{\mathrm{c}^2}{x-y}=1\).

Between the above two statements,