Question

A point $z$ is such that it is equidistance from three distinct points $z_1,z_2,z_3$
in Gaussian plane If $z,z_1,z_2$ are collinear, then Arg $\left(\frac{z_3-z_1}{z_3-z_2}\right)$ will be if $z_1,z_2,z_3$ are in anticlockwise sense.

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. $\frac{2\pi }{3}$

Answer 1

Answer: (A)

$\frac{\pi }{2}$

As z is equidistance from $z_1,z_2,z_3$ $\Rightarrow$ a circle with centre z and radius $|z_1-z|$ will passes through points $|z_1,z_2,z_3,|$with $z_{1}z{,}_2$ as end points of diameter. $\therefore$ Arg $\left(\frac{z_3-z_1}{z_{3-z_2}}\right)=\pi /2$