If I be the incentre of the triangle ABC, and a, b, c be the lengths of the sides BC, CA and AB respectively, then  equals

Concept:

Incentre:

The incentre of the triangle is the point of intersection of the internal bisector of angles

→ Also, it is a center of a circle touching all sides of the triangle.

→ coordinates of incentre are:

a, b, c: sides of ΔABC.

x_1, x₂, x₃ : x - coordinates of vertices

y₁, y₂, y₃: y - coordinates of vertices

AB = c

AC = b

BC = a

Angle bisector divides the opposite sides in the ratio of remaining sides

i.e., 

Calculation:

Let the incentre be at the origin and

Now 

the Incentre is

The Incentre is origin so,

From equation (1)

Option A is correct