TS EAMCET 03 May 2019 Shift 2 Solved Paper

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
√(‌

23

10

−‌

8

3

)2+(‌

7

10

−‌

1

3

)2
=‌

11√2

30