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 $(2 a, - 2 a),$ then find the orthocentre.

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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

(2 a, - 2 a),

then find the orthocentre.

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Question Text

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

(2 a, - 2 a),

then find the orthocentre.

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