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)

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

Since, the given triangle is an equilateral triangle. Therefore, incentre coincide with the centroid.
ie, $(\frac{1+0+2}{3},\frac{\sqrt{3}+0+0}{3})=(1,\frac{1}{\sqrt{3}})$