Question

Chords ac and bd intercept at e if ae=6 ec=12 and dc=18 how long is be

Answer 1

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.