Question

In $\Delta ABC$ if orthocentre be $(1,2)$ and circumcentre be $(0,0)$, the centroid of $\Delta ABC$ is

• A. $(\frac{1}{2},\frac{2}{3})$
• B. $(\frac{1}{3},\frac{2}{3})$
• C. $(\frac{2}{3},1)$
• D. none of these

Answer 1

The correct option is B $(\frac{1}{3},\frac{2}{3})$

Centroid $G$ divides orthocentre $H$ and circumcentre $O$ in the ratio $2:1.$

$G=(\frac{1\times 1+2\times 0}{3},\frac{2\times 1+2\times 0}{3})$

$=(\frac{1}{3},\frac{2}{3})$