# Find the x, when ray AN bisects the angle A by using the Angle bisector of a triangle Theorem

Notice that this question is related to the Angle bisector of a triangle Theorem

Let’s be ABC a triangle and Ray AN bisects the angle A

By Angle bisector of a triangle Theorem:

So, the equal ratios are:

We can write in form of ratios

\frac{BN}{NC}=\frac{AB}{AC}

Substitute the value of AB=21, AC=14, BN=9 and NC =x into the above expression:

\frac{\textcolor{tertiary}{9}}{x}=\frac{\textcolor{primary}{21}}{\textcolor{secondary}{14}}

After cross multiply, We get

21\times{x}=9\times{14}

both side divide by 21, we get:

{x}=\frac{\cancel{126}}{\cancel{21}}=6

Required value of x is 6.