Question

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

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

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.
$\therefore I\equiv \Bigg(\frac{0 + 1 + 2}{3},\frac{0+0+\sqrt{3}}{3}\Bigg)$
$\Rightarrow I \equiv(1/\sqrt{3})$