Answered

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

3 Chords WP And KZ Intersect At Point L In The Circle ShownWhat Is The Length Of KZa 7b 9C 10d 3 class=

Sagot :

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.

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