The co-ordinate of the centroid of the triangle is (‌
1+3+4
3
,‌
2−1+0
3
)=(‌
8
3
,‌
1
3
) If (h,k) be the circumcentre of the triangle, and have equal distance from all the points of triangle, OA=OB (h−1)2+(k−2)2=(h−3)2+(k+1)2 h2−2h+1+k2−4k+4=h2−6h+9+k2+2k+1 4h−6k=5 and OA=OC (h−1)2+(k−2)2=(h−4)2+k2 6h−4k=11 Solve the above two equations h=‌
23
10
,k=‌
7
10
Therefore, the distance between centroid and circumcentre √(‌