Given:
The figure of triangle GHI and a circle M inscribed in the triangle.
To find:
The perimeter of the triangle.
Solution:
We know that the lengths of the tangent on a circle from same exterior point are always equal.
(Tangent from point H)
Divide both sides by 4.
![x=5](https://tex.z-dn.net/?f=x%3D5)
Now,
![JH=6x-11](https://tex.z-dn.net/?f=JH%3D6x-11)
![JH=6(5)-11](https://tex.z-dn.net/?f=JH%3D6%285%29-11)
![JH=30-11](https://tex.z-dn.net/?f=JH%3D30-11)
![JH=19](https://tex.z-dn.net/?f=JH%3D19)
In the same way,
(Tangent from point H)
(Tangent from point H)
From the figure, it is clear that,
![IL=GI-GL](https://tex.z-dn.net/?f=IL%3DGI-GL)
![IL=40-GJ](https://tex.z-dn.net/?f=IL%3D40-GJ)
![IL=40-23](https://tex.z-dn.net/?f=IL%3D40-23)
![IL=17](https://tex.z-dn.net/?f=IL%3D17)
The perimeter of the triangle GHI is:
![Perimeter=GH+HI+GI](https://tex.z-dn.net/?f=Perimeter%3DGH%2BHI%2BGI)
![Perimeter=(GJ+HJ)+(HK+IK)+(GL+IL)](https://tex.z-dn.net/?f=Perimeter%3D%28GJ%2BHJ%29%2B%28HK%2BIK%29%2B%28GL%2BIL%29)
![Perimeter=(23+19)+(19+17)+(23+17)](https://tex.z-dn.net/?f=Perimeter%3D%2823%2B19%29%2B%2819%2B17%29%2B%2823%2B17%29)
![Perimeter=118](https://tex.z-dn.net/?f=Perimeter%3D118)
Therefore, the perimeter of the triangle GHI is 118 units.