In page no 49 of John B Conway's "Function of One Complex Variable" I fail to understand the theorem 3.14. In particular would anybody please explain me why do $w_2,w_3,w_4$ determine a circle $\Gamma'$? I have undestood that they are distinct but why are they describing a circle? It may be any curve in $\mathbb C_{\infty}$.
I am struggling hard to understand it but couldn't manage to find any reason. Please help me.
Thank you in advance.