What is the incentre of a triangle?

The incenter of a triangle is the point where the three angle bisectors of the triangle intersect. It is equidistant from all three sides of the triangle.

Here is how to understand it in detail:

Angle Bisectors: An angle bisector is a line or ray that divides an angle into two equal parts. In a triangle, there are three angles, and the angle bisectors of each of these angles intersect at a single point inside the triangle.

Properties of the Incenter:

The incenter is always located inside the triangle.
It is the center of the incircle, which is the largest circle that can fit inside the triangle, touching all three sides.
The incenter is equidistant from all three sides of the triangle. This means the perpendicular distance from the incenter to each of the three sides is the same.
Construction of the Incenter:

To locate the incenter, you need to construct the angle bisectors of each of the three angles of the triangle. The point where these three bisectors meet is the incenter.
You can also construct the incircle by drawing a circle with the incenter as its center, and its radius being the perpendicular distance from the incenter to any side of the triangle.
In summary, the incenter is the point of intersection of the angle bisectors of a triangle and is equidistant from the triangle's sides.