Question

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

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

Answer 1

Answer: (D)

$O A=2$
$O B=\sqrt{1+3}=2$
$A B=\sqrt{1+3}=2$

$O A=O B=A B$
$\therefore$ Triangle is equilateral.
Incentre $\left(\frac{0+2+1}{3}, \frac{0+0+\sqrt{3}}{3}\right)=\left(1, \frac{1}{\sqrt{3}}\right)$