Question

If the orthocenter of a triangle is $(6,3)$ and centroid is $(2,5)$, then find the circumcenter of the triangle.

• A. $(1,2)$
• B. $(1,3)$
• C. $(0,5)$
• D. $(0,6)$

Answer 1

The correct option is D $(0,6)$

Let the coordinates of circumcenter be $(x,y)$. Centroid divides the line joining orthocenter and circumcenter in the ratio $2:1$
$\therefore (2,5)=(\frac{2\times x+1\times 6}{2+1},\frac{2\times y+1\times 3}{2+1})$
$\Rightarrow (2,5)=(\frac{2x+6}{3},\frac{2y+3}{3})$
$\Rightarrow \frac{2x+6}{3}=2,\frac{2y+3}{3}=5$
$\Rightarrow x=0,y=6$
Thus, the circumcenter of the triangle is $(0,6)$