IR-TST 2017 Problem 16

There are $6$ points on the plane such that no three of them are collinear. It's known that between every $4$ points of them, there exists a point that it's power with respect to the circle passing through the other three points is a constant value $k$ .(Power of a point in the interior of a circle has a negative value.) Prove that $k=0$ and all $6$ points lie on a circle.

Proposed by Morteza Saghafian