Question

Find the measure of GH.

Answer 1

Answer:

D

Step-by-step 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

Answer 2

Answer:

$\textsf{GH=10}$

Step-by-step 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, $GH=-6+2(8)=$

$-6+16=$

$=10$

$\textsf{OAmalOHopeO}$