1 Answer

Melinda Green · Answer 1 · 2023-01-09T04:28:10+0000

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.

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