Question

If the lengths of the sides BC, CA and AB of a ΔABC are a, b and c respectively and AD is the bisector ∠A then find the lengths of BD and DC.

Answer 1

Let DC = X
∴ BD = a-X 

By using angle bisector there in ΔABC, we have 

`(AB)/(AC)=(BD)/(DC)` 

⇒ `c/b=(a-x)/x` 

⇒`cx=ab-bx` 

⇒`x(b+c)=ab` 

⇒`x=(ab)/(b+c)` 

Now,` a-x=a-(ab)/(b+c)` 

=`(ab+ac-ab)/(b+c)` 

=`(ac)/(a+b)`