How can the angle bisector theorem be used to locate the incentre of a triangle?

[logic19]

I while trying a hand on coordinate geometry concluded something which appeared amazing to me.There we can make significant use of angle bisector theorem in determining the incentre of a triangle.
Now suppose we have vertices given,or anything by which they can be concluded.
Now.by using the above stated theorem to determine any point of intersection of any angle bisector through a vertex on opposite side.(by theorem ratio and by section formulka the point.
now similarly on that angle bisector too an angle bisector from any of the two remaining sides will intersect and that point of intersection will be our incentre.Thus the required incentre can be obtained by same method as stated above.

 

[krateesh]

Well,good idea but u think that is peculiar actally it is very common,almost everybody here knows it,it is just a matter of chance that u studying at college level doesn't know such thing.

 

[tacman]

I agree that the use of the angle bisector theorem in determining the incentre of a triangle is quite fascinating. It is a useful tool in coordinate geometry and can help us locate the incentre with ease.

By using the angle bisector theorem, we can find the intersection point of any angle bisector through a vertex on the opposite side. This point can then be used to construct another angle bisector from one of the remaining sides, which will intersect at the incentre.

This method can be applied to any triangle, as long as we have the vertices or any other information that can help us determine them. It is a simple yet effective way of finding the incentre, and it shows the importance of the angle bisector theorem in geometry.

Thank you for sharing your insights on this topic. It is always exciting to discover new ways of approaching mathematical problems. Keep exploring and learning!