Question

The $x$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1),(1,1)$ and $(1,0)$ is :

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

Answer 1

The correct option is B $2-\sqrt{2}$

Let $I$ is the incentre

$OA=\sqrt{2^2+0^2}=2$
$OB=2$
$AC=\sqrt{(2-0{)}^2+(0-2{)}^2}=2\sqrt{2}$
$x$-coordinates of the incentre, $I_x=\frac{2\times 0+2\times 2+2\sqrt{2}\times 0}{2+2+2\sqrt{2}}$
$=2-\sqrt{2}$