The vertices of a triangle are (6,0),(0,6) and (6,6) . The distance between its circumcentre and centroid is

Step-by-step solution

Let the vertices of a triangle be A(6,0), B(0,6) and C(6,6) . array ll Now, & AB = 6²+6² =6 2 & BC = 6²+0 =6 and & CA = 0+6² =6 Also, & AB ²= BC ²+ CA ² array Therefore, ABC is right angled at C . So, mid point of A B is the circumcentre of A B C . Coordinate of circumcentre are (3,3) . Coordinate of centroid are, G ( 6+0+6 3 , 0+6+6 3 ) , ie, (4,4) Required distance = (4-3)²+(4-3)² = 2