Question

A triangle has corners at points A, B, and C. Side AB has a length of `18`. The distance between the intersection of point A's angle bisector with side BC and point B is `6`. If side AC has a length of `14`, what is the length of side BC?

Answer 1

`BC=10.667`

Explanation:

According to angle bisector theorem, in a `DeltaABC`, if angle `A` is bisected and it cuts `BC` at `D`, then

`(AB)/(AC)=(BD)/(DC)`

As `AB=18`, `AC=14` and distance between the intersection of point A's angle bisector with side BC and point B i.e. `BD` is `6`,

we have `18/14=6/(DC)`

or `DC=(14xx6)/18=(14xx1cancel6)/(3cancel18)=14/3=4.667`

Hence `BC=6+4.667=10.667`