Question

The vertices of a triangle are $A(0,0),B(0,2)$and $C(2,0),$ then find the distance between its orthocenter and circumcenter

• A. $0$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. None of these

Answer 1

The correct option is B

$\sqrt{2}$

Explanation for the correct option:

On plotting the above points, we get a right triangle.

So, the orthocenter for the given vertices of a triangle $=(0,0)$

Also, circumcenter $=\left[\frac{2+0}{2},\frac{0+2}{2}\right]=(1,1)$

Hence, the distance between the orthocenter and the circumcenter is

$$\begin{gathered} =\sqrt{{\left(1-0\right)}^2+{\left(1-0\right)}^2} \\ =\sqrt{1+1} \\ =\sqrt{2} \end{gathered}$$

So, the distance between the orthocenter and the circumcenter is $\sqrt{2}$

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