
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.
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