Question

The vertices of a triangle are $(6,0),(0,6)$ and $(6,6)$. The distance between its circumcenter and centroid is

• A. $2$
• B. $\sqrt{2}$
• C. $1$
• D. $2\sqrt{2}$

Answer 1

The correct option is B

$\sqrt{2}$

Explanation for the correct option:

Given that the vertices $(6,0),(0,6)$ and $(6,6)$ form a right angled triangle.

The point $(6,0),$ and $(0,6)$ gives the diameter of the circumcircle

Hence, the circumcenter $=\left(\frac{0+6}{2},\frac{6+0}{2}\right)=(3,3)$

Centroid of a triangle $=\left(\frac{0+6+6}{3},\frac{6+0+6}{3}\right)=(4,4)$

Thus, the distance between the circumcenter and centroid of a triangle is

$$\begin{gathered} =\sqrt{{\left(4-3\right)}^2+{\left(4-3\right)}^2} \\ =\sqrt{1+1} \\ =\sqrt{2} \end{gathered}$$

Hence the correct option is $\mathrm{Option}\left(\mathrm{B}\right)$