Question

Three concurrent lines are drawn from vertices $A(1,2),B(2,3)$ and $C(3,7)$ of $△ABC$ 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 $△OPQ$ be point $R$. If orthocentre of $△PQR$ be $(a,b)$, then find $a+b$.

Answer 1

Answer: 6

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