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  4. Three concurrent lines are drawn from vertices A (1,2), B (2,3) and C (3,7) of triangle ABC which divide the triangle into 6 parts having equal areas and point of concurrency is point O. Let P(-5,4) and Q(-3,7) be two points such that orthocentre of triangle O P Q be point R. If orthocentre of triangle P Q R be ( a , b ), then find a + b.

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Q. Three concurrent lines are drawn from vertices $A (1,2), B (2,3)$ and $C (3,7)$ of $\triangle ABC$ which divide the triangle into 6 parts having equal areas and point of concurrency is point $O$. Let $P(-5,4)$ and $Q(-3,7)$ be two points such that orthocentre of $\triangle O P Q$ be point $R$. If orthocentre of $\triangle P Q R$ be $( a , b )$, then find $a + b$.

Straight Lines

Solution:

Clearly point of concurrency will be centroid, $O =(2,4)$ and clearly orthocentre of $\triangle PQR$ will be point $O$.
$\therefore a + b =6 $