Given:
[tex]QP=2x+9,QM=5x-3[/tex]
To find:
The value of QN.
Solution:
From the figure it is clear that, point Q is the intersection point of angle bisectors. So, point Q is the incenter.
[tex]QP=QM=QN[/tex] ...(i) [Incenter is equidistant from each side of triangle]
Using (i), we get
[tex]QP=QM[/tex]
[tex]2x+9=5x-3[/tex]
[tex]2x-5x=-9-3[/tex]
[tex]-3x=-12[/tex]
Divide both sides by -3.
[tex]x=4[/tex]
Now,
[tex]QP=2x+9[/tex]
[tex]QP=2(4)+9[/tex]
[tex]QP=8+9[/tex]
[tex]QP=17[/tex]
Using (i), we get
[tex]QN=17[/tex]
Therefore, the value of QN is 17.
