$z_1,z_2,z_3$  are three non-zero distinct affixes satisfying  $|z-1|=1\&z_2^2=z_1{z}_3$ then

(Note : arg (z) represents principle argument of z;   
$\arg \left(z\right)\in (-\pi ,\pi ]$

1^st option – chord  $(Z_3-Z_2)$ is $\perp$  to line joining   $\frac{z_2+z_3}{2}$and 1.
 
2^nd option – angle by chord  $(Z_3-Z_2)$ at $(1,0)$  is double of angle at  $(0,0)$
4^th option – Ptolemy’s theorem