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Chords WP and KZ intersect at point L in the circle shown.Wz*3x - 22KIL5РWhat is the length of KZ?7.5910O 12

Chords WP and KZ intersect at point L in the circle shown.Wz*3x - 22KIL5РWhat is the-example-1
User Mdmb
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1 Answer

4 votes

For the cicle with intersecting chords the relation between the length of segments of chords is,


KL\cdot ZL=WL\cdot PL

Substitute the values in the equation and solve for x.


\begin{gathered} 2\cdot(3x-2)=x\cdot5 \\ 6x-4=5x \\ 6x-5x=4 \\ x=4 \end{gathered}

So value of x is 4.

The equation for the length of chord KZ is,


\begin{gathered} KZ=KL+LZ \\ =2+3x-2 \\ =3x \end{gathered}

Substitute the value of x in equation to determine the length of KZ.


\begin{gathered} KZ=3\cdot4 \\ =12 \end{gathered}

So answer is 12.

User Melinda Green
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