Question:

Let $\alpha\in\mathbb{R}$, $z_1,z_2,z_3$ be three distinct complex numbers such that $|z_1|=|z_2|=|z_3|=3$ and $|(kz_1+z_2)-(kz_2+z_3)|_{\min}=\alpha|z_3-z_2||z_3-z_1|$, $\forall k\in\mathbb{R}-\{0\}$. Then $36\alpha=$