Question

The incentre of the triangle with vertices $(1,\sqrt{3}),(0,0)$ and $(2,0)is$

• A. $(1,\frac{\sqrt{3}}{2})$
• B. $(\frac{2}{3},\frac{1}{\sqrt{3}})$
• C. $(\frac{2}{3},\frac{\sqrt{3}}{2})$
• D. $(1,\frac{1}{\sqrt{3}})$

Answer 1

Answer: (D)

Let the vertices of triangle be $A(1,\sqrt{3}),5(0.0)$ and $C(2,0)$. Here, $AB=BC=CA=2$
Therefore, it is an equilateral triangle. So, the in centre coincides with centroid.
$\therefore I\equiv (\frac{0+1+2}{3},\frac{0+0+\sqrt{3}}{3})$
$\Rightarrow I\equiv (1/\sqrt{3})$