Is it geometry?

Geometry Level 4

$\begin{cases} { x }^{ 2 }+{ y }^{ 2 }={ z }^{ 2 } \\ { y }^{ 2 }-yz+{ z }^{ 2 }={ x }^{ 2 } \\ { z }^{ 2 }+k·zx+{ x }^{ 2 }={ y }^{ 2 } \end{cases}$

Let $x$ , $y$ , $z$ positive numbers the satisfy the system of equations above.

If this system has at least one solution, what is the value of $k$ ?