If the circumcenter of an acute-angled triangle lies at the origin and the centroid is the middle point of the line joining the points `(a^2+1,a^2+1)` and `(2a ,-2a),` then find the orthocentre.

Explanation

Circumcentre is `O(0,0)`
Centroid `G=((a+1)^2/(2),(a-1)^2/(2))` (midpoint of given points)
Points H,G and O are collinear with `HG:GO=2:1`.
So, using section formula, we have orthocentre as `H((3(a+1)^2)/(2),(3(a-1)^2)/(2))`