AP EAMCET Engineering 2018 Apr 22 Shift 2 Paper

The centroid of a non-equilateral triangle divides the line orthocenter and circumcentre in 2:1, thus, the coordinates of circumcentre is (h, k), then
(

2+5

3

,

2k+8

3

)=(3,

14

3

)
(h,k)=(2,3)
The image of orthocenter (5, 8) with respect to side BC,
So, the radius of circumcircle of ∆ABC is
√(8−2)2+(5−3)2=√40 =2√10
So, the diameter is 4√10.