What is the length of the tangent line in the picture?

x = -2

Step-by-step explanation:

The tangent line has length "x + 8"

The secant line has length "x + 6 + 5", where

5 is the inner part

x + 6 is the outer part

Now,

the secant-tangent theorem tells us that square of the tangent line is equal to the outer segment of secant line multiplied by length of whole secant line.

So, we can say:

We can solve for x shown below:

The value of x is -2