To solve this problem we have to use the intersecting chords theorem which states a proportion between the four resulting segments,
Based on this theorem, we can define the following proportion
[tex]VM\times VN=KV\times VJ[/tex]
First, we find VK. We have to replace the given information
[tex]\begin{gathered} 18\times22.5=KV\times9 \\ KV=\frac{405}{9}=45 \end{gathered}[/tex]
Now, by the sum of segments, we define an equation for JK.
[tex]\begin{gathered} JK=VJ+KV \\ JK=9+45=54 \end{gathered}[/tex]
Therefore, the chord JK is 54 units long.
