Question

What is the length of line segment DG
A)4units
B)7units
C)12units
D)23units

Answer 1

Answer: Option 'C' is correct.

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.

`GF* GE=GH* GD\\\\6(x+6)=5(x+8)\\\\6x+36=5x+40\\\\6x-5x=40-36\\\\x=4\ units`

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

`DG=x+5+3=x+8=4+8=12\ units`

Hence, Option 'C' is correct.

Answer 2

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

We have

`EG = 6+x`

`FG = 6`

`GD = 5+x+3`

`HG = 5`

EG×FG=GD×HG

`6(6+x)=5(x+8)`

`36+6x=5x+40`

`6x-5x=40-36`

`x=4`

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

Answer: C