There is a quite useful theorem to solve this kind of problems, it's called the 'Intersecting chords theorem' and, adapted to the circle in the image, it's:
[tex]PL\cdot LW=KL\cdot LZ[/tex]
So, using the lengths given by the problem:
[tex]\begin{gathered} x\cdot2=1\cdot(3x-3) \\ \Rightarrow2x=(3x-3) \\ \Rightarrow x=3 \end{gathered}[/tex]
Finally, we can calculate KZ
[tex]\begin{gathered} KZ=KL+LZ \\ \Rightarrow KZ=1+(3x-3)\text{ with x=3} \\ \Rightarrow KZ=1+(9-3)=7 \end{gathered}[/tex]
So, from the set of possible answers, the right choice is a.
