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Centroid of a Triangle

If the circum...

Question

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 line on which the orthocenter lies

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Solution

H is orthocenter
G is centroid
O is circumcenter

$\frac{H G}{G O} = \frac{2}{1}$

Therefore coordinates of orthocenter

$(\frac{3 (a^{2} + 1)}{2}, \frac{3 (a^{2} - 1)}{2})$

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