Respuesta :

merlynthewhizz
The circle theorem used for this problem is shown in the diagram below

We have
[tex]EG = 6+x [/tex]
[tex]FG = 6[/tex]
[tex]GD = 5+x+3[/tex]
[tex]HG = 5[/tex]

EG×FG=GD×HG
[tex]6(6+x)=5(x+8)[/tex]
[tex]36+6x=5x+40[/tex]
[tex]6x-5x=40-36[/tex]
[tex]x=4[/tex]

Length of DG = 4+3+5=12 units

Answer: C

Ver imagen merlynthewhizz

Answer: Option 'C' is correct.

Step-by-step explanation:

Since we have given that

EF and DG are two secants intersects at G.

EF = x

FG = 6

EG = x+6

DH = x+3

GH = 5

DG = x+3+5=x+8

And we know the "Intersecting Secant theorem", which concludes that the product of their segments will be equal to each other.

[tex]GF\times GE=GH\times GD\\\\6(x+6)=5(x+8)\\\\6x+36=5x+40\\\\6x-5x=40-36\\\\x=4\ units[/tex]

But we need to find the value of DG which is given by

[tex]DG=x+5+3=x+8=4+8=12\ units[/tex]

Hence, Option 'C' is correct.

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