Find the incentre of the triangle with vertices `A91,sqrt3), B(0,0)` and `C(2,0)`.

Options

A. `(1,sqrt(3)//2)`
B. `(2//3,1,sqrt(3))`
C. `(2//3,sqrt(3)//2)`
D. `(1//1,sqrt(3))`

Answer

D

Explanation

Let the vertices of the triangle be `A(1,sqrt(3)),(B(0,0) and C(2,0)`. We observe that
`AB=2=BC=AC`
So, the triangle is equilateral. Consequently, its incetnre coincides with the whose coordinates are
`((1+0+2)/(3),(sqrt(3)+0+0)/(3))=(1-(1)/(sqrt(3)))`