To solve the problem of finding the length of segment (AB), we assume a common scenario involving a circle, diameter, and perpendicular chord (a typical problem context). Here's the step-by-step solution:

Problem Statement (Assumed)

(AB) is the diameter of a circle with center (O). Chord (CD) is perpendicular to (AB) at point (E). If (CE = 4) cm and (AE = 2) cm, find the length of (AB).

Solution

1. Define Variables: Let the radius of the circle be (r) cm. Then, (AB = 2r) (diameter = 2×radius).
2. Distance from Center to Point (E): Since (OA = r) and (AE = 2) cm, (OE = OA - AE = r - 2) cm.
3. Right Triangle (OEC): Chord (CD \perp AB), so (\triangle OEC) is right-angled. Using the Pythagorean theorem:
   [OC^2 = OE^2 + CE^2]
   Substitute (OC = r), (OE = r-2), (CE = 4):
   [r^2 = (r-2)^2 + 4^2]
4. Simplify:
   [r^2 = r^2 -4r +4 +16]
   [0 = -4r +20]
   [r = 5]
5. Length of (AB): (AB = 2r = 2×5 = 10) cm.

Answer: (\boxed{10}) cm.

(Note: If the problem context differs, adjust the approach based on the given figure, but this is a standard solution for a common segment length problem.)
(\boxed{10})

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