Question

The incentre of the triangle with 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)

$\left( 1,\frac{1}{\sqrt{3}} \right)$

Answer 2

$\because$ Here $AB = BC = CA$

$\therefore$ The triangle is equilateral .

So, the incentre is the same as the centroid.

∴ Incentre =$\left( \frac{1 + 0 + 2}{3},\frac{\sqrt{3} + 0 + 0}{3} \right) = \left( 1,\frac{1}{\sqrt{3}} \right)$