The length of the segment AC is 4√3, so the correct option is E.
How to get the length of AC?
In the image, you can see a right triangle.
We do know that AB = 8 units, and BC is equal to the radius of the circle.
We also know that the area of the circle is 16pi, and the area of a circle of radius R is:
A = pi*R^2
Replacing our area, we get:
16pi = pi*R^2
16 = R^2
√16 = R = 4.
So the radius of the circle is 4, which means that BC = 4.
Now we can use the Pythagorean theorem, that says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, this can be written as:
AB^2 = BC^2 + AC^2
8^2 = 4^2 + AC^2
64 - 16 = AC^2
√48 = AC
√(3*16) = AC
4√3 = AC
So the correct option is E.
If you want to learn more about right triangles, you can read:
https://brainly.com/question/2217700
