In the image, we see a circle with center $C$ and radius $DC$. Chord $AB$ is constructed such that it is perpendicular to radius $DC$ at point $E$, and the length of segment $AE$ is given as 8 inches.

To find the length of segment $BE$, we can use the fact that the perpendicular from the center of a circle to a chord bisects the chord. Since $AE = 8$, it follows that $BE = AE$, because the perpendicular bisects the chord into two equal segments.

Thus, $BE = 8$ inches.

So, the correct answer is:

• Segment BE is 8 inches.

Would you like further details on this type of problem or help with similar concepts?

Here are some additional related questions you may find helpful:

1. Why is the perpendicular from the center of a circle to a chord always bisecting the chord?
2. How does the Pythagorean theorem apply in this case, and where would it be used?
3. Can you solve for the radius of the circle if we were given a different set of measurements?
4. How do we calculate the length of a chord in a circle if we know the radius and perpendicular distance from the center to the chord?
5. What properties do we use in solving problems with perpendiculars drawn to chords?

Tip: Always look for symmetry in geometry problems involving circles. The perpendicular from the center to a chord often creates equal segments.