Is it geometry?

Geometry Level 4

{x2+y2=z2y2yz+z2=x2z2+kzx+x2=y2\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 xx,yy,zz positive numbers the satisfy the system of equations above.

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

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