Question

What is the length of Line KZ?

Answer 1

Length of Chord KZ = 12

Explanation:

Given that chords WP and KZ intersect each other at point L,

Chord WP is divided into two segments, segment WL and PL

Chord KZ is divided into segment KL and ZL.

According to the Intersecting Chord Theorem,

the product of the segments of Chord KZ = the product of the segments of Chord WP

Thus,

`2*(3x -2) = x*5`

Solve for x

`6x - 4 = 5x`

Add 4 to both sides

`6x - 4 + 4 = 5x + 4`

`6x = 5x + 4`

Subtract 5x from both sides

`6x - 5x = 5x + 4 - 5x`

`x = 4`

=>Length of Chord KZ = 2 + (3x - 2)

Plug in the value of x

`= 2 + (3(4) - 2)`

`= 2 + (12 - 2)`

`= 2 + 10`

`length of Chord KZ = 12`