Answer:
The length of BE is 5.5 units.(A correct option)
Step-by-step explanation:
Given diameter AC intersects chord BD at point E such that AE = 2.5 units and DE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. we have to find the approximate length of BE.
CE=CO+OE=5+(OA-AE)=5+2.5=7.5 units.
Now, by Intersecting Chord Theorem which states that when two chords intersect each other inside a circle then the products of their segments are equal.
⇒ [tex]CE\times AE=BE\times DE[/tex]
⇒ [tex]7.5\times 2.5=BE\times 3.4[/tex]
⇒ [tex]BE=\frac{7.5\times 2.5}{3.4}=5.5147\sim5.5units[/tex]
Hence, the length of BE is 5.5 units.
