Question

Find the measure of GH.

Answer 1

`\textsf{GH=10}`

Explanation:

`(EF)^(2) =FG(FH)`

`(12)^(2) =8(8-6+2x)`

`144=8(2+2x)`

`144=16+16x`

`16x=144-16`

`16x=128`

`x=128/16=8`

So,
`GH=-6+2(8)=`

`-6+16=`

`=10`

`\textsf{OAmalOHopeO}`

Answer 2

D

Explanation:

Given a tangent and a secant from an external point to the circle, then

The product of the external part and the whole secant is equal to the square of the tangent, that is

8(8 - 6 + 2x) = 12²

8(2 + 2x) = 144 ( divide both sides by 8 )

2 + 2x = 18 ( subtract 2 from both sides )

2x = 16 ( divide both sides by 2 )

x = 8

Then

GH = - 6 + 2x = - 6 + 2(8) = - 6 + 16 = 10 → D