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(x1,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