if G is the centroid and I the incentre of the triangle with vertices A(-36,7) ,B(20,7) ,C(0,6) then find the value of GI?
↵We know centroid G of a triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is (x1+x2+x3/3, y1+y2+y3/3) Therefore here co-ordinates of G is (-16/3, 2). If a, b and c are the lengths of opposite sides of vertices (x1, y1), (x2, y2) and (x3, y3) respectively then in-centre will be given by (ax1+bx2+cx3/a+b+c, ay1+by2+cy3/a+b+c). Here a=25, b=39, c=56 and a+b+c = 120. Therefore co-ordinates of I = (-1, 0). So, GI= (sqt of 205)/3.