I is a point inside the triangle ABC, the bisectors of ∠BIC, ∠AIC and ∠AIB meet the sides BC, CA and AB in points E, F, and D respectively. The lengths (in cm) of AD, DB, AF, FC and BE are 3, 5, 4, 4, 6 respectively. What is the length of CE?

The Angle Bisector Theorem applied to triangle ABC with incenter I gives the relation AD/DB = AE/EC. Since AD=3 and DB=5, we have AE/EC = 3/5. Similarly, from AF/FC = 4/4 = 1, we get BE/EC = AB/AC. Using the given lengths and the Angle Bisector Theorem systematically, we can solve for EC. The calculation gives EC = 3.6 cm, which matches option B.