Question

In the diagram, if EC = 8, ED = 6 and AE = 12 solve for EB.

Answer 1

The length of segment EB = 4 units

Explanation:

From the figure we can see a circle with two chords intersects each other.

The products of segments of chords are equal

To find the length of EB

we have EC = 8, ED = 6 and AE = 12

From the figure we can write,

AE * EB = EC * ED

EB = (EC * ED)/AE

= (8 * 6)/12 = 4 units

Therefore the correct answer is EB = 4 units

Answer 2

The length of segment EB = 4

Explanation:

* Lets revise a fact in the circle

- When two chords intersect each other inside a circle, the

products of their segments are equal

* Now lets use this fact to solve the problem

- AB and CD are two chords in the circle intersect each other

at point E

- The segments of AB are AE and EB

- The segments of CD are CE and ED

* From the fact above

∴ AE × EB = CE × ED

∵ AE = 12 units

∵ EC = 8 units and ED = 6 units

∴ 12 × EB = 8 × 6

∴ 12 EB = 48 ⇒ divide both sides by 12

∴ EB = 4

* The length of segment EB = 4