Option A:
The length of BE is 4.
Solution:
Given data:
AE = 6, EC = 12 and DE = 18
To find the length of BE:
If two chords intersect in a circle, then the product of lengths of one segment is equal to the product of lengths of other segment.
⇒ AE × EC = DE × BE
⇒ 6 × 12 = 18 × BE
⇒ 72 = 18 × BE
Divide by 18 on both sides of the equation.
⇒ 4 = BE
Switch the sides.
⇒ BE = 4
The length of BE is 4.
Option A is the correct answer.
