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 ) = BC×Ax + CA × Bx + AB × CxP , BC×Ay + CA × By + AB × CyP 

Here Ax , Bx and Cx are x coordinates of vertices A , B and C respectively
And
Ay , By and Cy 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 ) = aX1 + bX2 + cX3a + b + c , aY1 + bY2 + cY3a + b + c                                                         ( Ans )

 

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