If `z_1, z_2, z_3, z_4` are the affixes of four point in the Argand plane, `z` is the affix of a point such that `|z-z_1|=|z-z_2|=|z-z_3|=|z-z_4|` , then prove that `z_1, z_2, z_3, z_4` are concyclic.

Explanation

We have,
`|z-z_(1)|=|z-z_(2)|=|z-z_(3)|=|z-z_(4)|`
Therefore, the point having affix z is equidistant from the four points having affixes `z_(1),z_(2),z_(3),z_(4).` Thus, z is the affix of either the center of a circle or the point of intersection of diagonals of a rectangle. Therefore, `z_(1),z_(2),z_(3),z_(4)` are concyclic.