coordinates of vertices of triangle ABC are A(X1,Y1),B(X2,Y2),C(X3,Y3). if BC=a.CA=b and AB=c, then find the coordinates of the incentre of triangle ABC.

Answer :

Given coordinates of vertices of triangle  =  A( X₁ , Y₁ )  , B ( X₂ , Y₂ )  and C ( X₃ , Y₃ )  , And BC   = a , CA  =  b and AB  =  c
And we know formula for coordinates of incenter , As :

Let incenter at " O "  , So

O ( X  , Y ) = $\left(\frac{BC\times A_x + CA \times B_x + AB \times C_x}{P} , \frac{BC\times A_y + CA \times B_y + AB \times C_y}{P}\right)$

Here A_x , B_x and C_x are x coordinates of vertices A , B and C respectively
And
A_y , B_y and C_y are y coordinates of vertices A , B and C respectively .
And
P  =  Perimeter of triangle  =  AB  +  BC  +  CA 

So,
Coordinates of Incenter O ( X  , Y ) = $\left(\frac{a{X}_1 + b{X}_2 + c{X}_3}{a + b + c} , \frac{a{Y}_1 + b{Y}_2 + c{Y}_3}{a + b + c}\right)$                                                        ( Ans )