Question

What is #2 ? In the figure shown , QP = 2x + 9 and QM = 5x - 3 FIND QN

Answer 1

Given:

`QP=2x+9,QM=5x-3`

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.

`QP=QM=QN` ...(i) [Incenter is equidistant from each side of triangle]

Using (i), we get

`QP=QM`

`2x+9=5x-3`

`2x-5x=-9-3`

`-3x=-12`

Divide both sides by -3.

`x=4`

Now,

`QP=2x+9`

`QP=2(4)+9`

`QP=8+9`

`QP=17`

Using (i), we get

`QN=17`

Therefore, the value of QN is 17.