Find the coordinates of the centre of the circle inscribed in a triangle whose vertices are (-36, 7), (20, 7) and (0, -8).

Key points to solve the problem:

• The idea of distance formula- Distance between two points P(x₁,y₁) and Q(x₂,y₂) is given by- PQ =

•

Incentre of a triangle - Let A(x_1,y₁) , B(x₂,y₂) and C(x₃,y₃) be the 3 vertices of ΔABC and O be the centre of the circle inscribed in ΔABC

O = where a, b and c are length of sides opposite to ∠ A , ∠ B and ∠ C respectively.

Given, coordinates of vertices of the triangle as shown in figure:

We need to find the coordinates of O:

Before that, we have to find a ,b and c. We will use the distance formula to find the same.

As, a = BC =

b = AC =

and c = AB =

∴ coordinates of O =

…ans