Question

In the given figure, AD is the bisector of `angle BAC`. If AB =10 cm , AC=6 cm and BC=12 cm, find BD and DC .

Answer 1

Let BD= x cm. then.
`DC=(BC-BD)=(12-x)cm.`
In `Delta ABC, AD` is the bisector of `angle BAC`.
So, by angle-bisector theorem, we have

`(BD)/(DC)=(AB)/(AC)rArr (x)/(12-x) =(10)/(6)`
`rArr 6x=10(12-x)`
`rArr 16x=120 rArr x=7.5`
Hence, `BD=7.5 cm, and DC=(12-7.5) cm, =4.5 cm`