Question

If $z_1,z_2,z_3\text{and}{z}_4$ are the affixes of four points in the argand plane and $z$ is the affix of a point such that $|z-z_1|=|z-z_2|=|z-z_3|=|z-z_4|$, then $z_1,z_2,z_3,z_4$ are

• A. Concylic
• B. Vertices of a parallelogram
• C. Vertices of a rhombus
• D. In a straight line

Answer 1

The correct option is A Concylic

Since $z$ is equidistant from $z_1,z_2,z_3,z_4$ it can be said that $z_1,z_2,z_3,z_4$ are concyclic or either vertices of square. Considering those points to be concyclic $z$ is the center either $|z_0-z_i|$ to be radius where $i=1,2,3,4$, either of them.