# The Incentric incentre

• logic19
In summary, the conversation discusses the use of the angle bisector theorem in determining the incentre of a triangle in coordinate geometry. It is explained that any point of intersection of an angle bisector through a vertex on the opposite side can be found using the theorem's ratio and section formula. The same method can be applied to find the incentre by using an angle bisector from any of the remaining sides. It is mentioned that this is a common knowledge and not a peculiar idea.

#### 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.

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.

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!

## What is the Incentric Incentre?

The Incentric incentre is a point of concurrency in a triangle that is the center of the inscribed circle, also known as the incircle. It is the point where the angle bisectors of the triangle intersect.

## How is the Incentric Incentre different from the Centroid and Circumcentre?

The Incentric incentre is different from the centroid and circumcentre because it is not a center of symmetry. It is also not necessarily located within the triangle, unlike the centroid and circumcentre which are always inside the triangle.

## What is the significance of the Incentric Incentre?

The Incentric incentre is important in geometry because it is used to construct the incircle, which is the largest circle that can fit inside a triangle. It is also used in various geometric proofs and constructions.

## How is the Incentric Incentre calculated?

The coordinates of the Incentric incentre can be calculated using the formula:
x = (aAx + bBx + cCx) / (a + b + c)
y = (aAy + bBy + cCy) / (a + b + c)
where a, b, and c are the lengths of the sides of the triangle and A, B, and C are the vertices.

## What is the relationship between the Incentric Incentre and the Excentric Excentre?

The Incentric incentre and the Excentric excentre are both points of concurrency in a triangle, but they have different properties. The Incentric incentre is the center of the incircle, while the Excentric excentre is the center of the excircle, which is the circle tangent to all three sides of the triangle. The Incentric incentre is also always inside the triangle, while the Excentric excentre can be located outside the triangle.