Plz solve!!!

Answer:
Given
AD is interior angle bisector of angle A .
AE is exterior angle bisector of angle A .


In $∆$ ABC

$\frac{AB}{AC} = \frac{BD}{CD}$                     ------- ( 1 )          ( By angle bisector theorem ) 

$\frac{AB}{AC} = \frac{BE}{CE}$                    -------- ( 2 )          ( By exterior angle bisector theorem )

Now from equation 1 and 2 we get

$\frac{BD}{CD} = \frac{BE}{CE}$

$\Rightarrow$$\frac{BD}{BE} = \frac{CD}{CE}$                    ( As we know $\frac{a}{b } = \frac{c}{d} \Rightarrow \frac{a}{c} = \frac{b}{d}$     )
So,

BD : BE  = CD : CE                                       ( Hence proved )