Question

The vertices of a triangle are $A(0,0),B(0,2)$ and $C(2,0)$. The distance between circumcenter and orthocenter is:

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

Answer 1

The correct option is A $\sqrt{2}$

Clearly given triangle is an isosceles right angle triangle .
So, we know that orthocentre will be at vertices $A$ i.e $(0,0)$.

(At which angle is ${90}^0$)
And circumcenter will be mid point of hypotenuse i,e $(1,1)$
Thus required distance is $=\sqrt{1^2+1^2}=\sqrt{2}$