Hello math bugs(🐞) and Hivers(🐝)
I hope you all are strong and stout.

My last post was about cir-cim-circle and today I have come up with **in-circle** and its properties.

We can take any kind of triangle and if we bisects any two angles, the bisectors will meet a point **always inside the triangle** and the point is called **in centre**. We can also draw three bisectors of the three angle of a triangle. The sides of the taken triangle are always equidistance from the IN-CENTRE and the distance is called in-radius. Hence taking the radius if we draw a circle ,it will thus be an in-circle the triangle.
![img_0.02870713538584054](https://images.ecency.com/DQmWuDDecxucPha8oCstetf1ubWv96NdujiZSYJKQDZm4Ee/img_0.02870713538584054.jpg)
If the length of perimeter of the triangle be 2S
Then semi-perimeter (S)= (a+b+c)/2
**Hence,**
Area of the ∆ABC in the figure below is **(∆)** = **r.s**
Check it below:

![img_0.5813166761679841](https://images.ecency.com/DQmVuwFr1EZ3jCZ4fhtLDyZ9HnRt8TyBxqcLqX7XCSRaVYL/img_0.5813166761679841.jpg)
**Things to be considered:**
1) The triangle may be equilateral, isosceles, scalance is all cases unlike cir-cum-circle **the in-centre** is always inside the triangle.The same is for right angle triangle also.
2) It is not necessary a in-radius touch a side of a triangle on the mid point. In case of equilateral triangle it touches the mid point.
3) It is not necessary the angle bisectors touch vertices of a circle though in case of equilateral triangle it touches.

Find the area of the following triangle:
![img_0.2807067980303392](https://images.ecency.com/DQmQEmYQq4Bszu7tdeSPaqZn2tzTjaSUjzXyz7pupoCr9R7/img_0.2807067980303392.jpg)
 Your Options are: 

1) 44 square cm
2) 46 square cm
3) 48 square cm
4) 50 square cm

My next topic will be centroid or geo-centre.

Thank you for visiting 

Stay healthy 

See you around 

Regards: @meta007