# how to find incentre of triangle when three vertices are given

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

The significance of the incentre is a point where the radius must be drawn from to have the biggest possible circle which touches all of the sides of the triangle.
The incentre always remains inside the triangle as the name suggests because the circle it is the centre of must be located inside the triangle
After we tested the four different triangles (2 by computer 2 by hand) the significance of the incentre we stated at the beginning was correct; the incentre is a point which always remains within the triangle and is the point where the radius must be drawn from to have the biggest possible circle which touches all of the sides of the triangle.

Neer Varshney
76 Points
13 years ago

Let the triangle be ABC in which vertices are A(x1,y1), B(x2,y2) and C(x3,y3).

`Let AB= a.

BC= b.

AC= c.

Then

Incenter(x,y) = ( ax1+bx2+cx3)/(a+b+c) , (ay1+by2+cy3)/(a+b+c)).