Question

If the orthocenter and centroid of a triangle are (–3, 5) and (3, 3) respectively then the circumcenter is

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

Answer 1

The correct option is D (6,2)

Since the centroid divides the line joining orthocenter and circumcenter in the ratio 2:1,
$\therefore$ If circumcenter is $\alpha ,\beta$ then
$3=\frac{2.\alpha +1.(-3)}{2+1}\Rightarrow 2\alpha =9+3and3\frac{2.\beta +1.5}{2+4}\Rightarrow 2\beta =9-5\therefore \alpha =6,\beta =2\therefore Circumcentreis(6,2).$