coordinates of the centres related to triangle

centroid ((x1+x2+x3)/3, (y1+y2+y3)/3)

In-centre

A(x1,y1)

B(x2,y2)

C(x3,y3)

Incentre ((ax1+bx2+cx3)/(a+b+c), (ay1+by2+cy3)/(a+b+c))

Ex centres

centre of the escribed circle opposite to the angle A

((-ax1+bx2+cx3)/(-a+b+c), (-ay1+by2+cy3)/(-a+b+c))