Question

The centroid of the triangle is $(3,3)$ and the orthocentre is $(3,-5)$, then its circumcentre is

• A. $(0,4)$
• B. $(0,8)$
• C. $(6,2)$
• D. $(6,-2)$

Answer 1

The correct option is C $(6,2)$

Centroid divides the line joining orthocentre and circumcentre in the ratio $2:1$

Let the circumcentre be $(x,y)$

Then by section formula, we get

$\frac{(2x+3)}{3}=3$

$⟹2x+3=9$

$⟹x=3$

And $\frac{2y-5}{3}=3$

$⟹2y-5=9$

$⟹y=7$

Hence, the circumcentre is $(3,7)$.