Question

3. Chords WP and KZ intersect at point L in the circle shown.What is the length of KZ?a. 7b. 9C. 10d. 3

Answer 1

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:

`PL\cdot LW=KL\cdot LZ`

So, using the lengths given by the problem:

`\begin{gathered} x\cdot2=1\cdot(3x-3) \\ \Rightarrow2x=(3x-3) \\ \Rightarrow x=3 \end{gathered}`

Finally, we can calculate KZ

`\begin{gathered} KZ=KL+LZ \\ \Rightarrow KZ=1+(3x-3)\text{ with x=3} \\ \Rightarrow KZ=1+(9-3)=7 \end{gathered}`

So, from the set of possible answers, the right choice is a.