Question

In a ΔABC, AD is the bisector of ∠A. If AB = 10 cm, AC = 14 cm and BC = 6 cm, find BD and DC.  

 

Answer 1

It is given that AD bisects ∠𝐴.
Applying angle – bisector theorem in Δ ABC, we get:
`(BD)/(DC)=(AB)/(AC)`
Let BD be x cm.
Therefore, DC = (6- x) cm
⟹ `x/(6-x)=10/14`
⟹14x = 60-10x
⟹24x = 60
⟹x = 2.5 cm
Thus, BD = 2.5 cm
DC = 6-2.5 = 3.5 cm