If the orthocentre and centroid of a triangle are (-3,5) and (3,3) respectively. Find its circumcenter.

centroid divides line joining orthocentre and circumcentre in the ratio 2:1.

let the circumcentre be (x,y)

 

applying section formula

 

(2x-3)/3=3

or,x=6

 

(2y+5)/3=3

or, y=2

 

therefor circumcenter=(6,2)