Answer:
The length of segment EB = 4
Step-by-step 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
