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 $2-\sqrt{2}$

Corrdinates of the vertices of the triangle whose mid points are
$(0,1),(1,1)$ and $(1,0)$ are $(0,2),(0,0)$ and $(2,0)$ respectively
$X$ -coordinate of incentre is
$=\frac{{ax}_1+b{x}_2+{cx}_3}{a+b+c}$
$=\frac{2\times 2+2\sqrt{2}\times 0+2\times 0}{2+2+2\sqrt{2}}$
$=\frac{4}{4+2\sqrt{2}}=\frac{2}{2+\sqrt{2}}=2-\sqrt{2}$