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 `A(1, sqrt(3)), B(0,0) and C(2,0)` be the vertices of `DeltaABC`. Then,
`a=BC=2,b=AC= 2 and c=AB=2`
`rArr AB=BC=CA`
`rArr DeltaABC` is equilateral.
Hence, the incentre is same as the centroid whose coordinates are
`((1+0+2)/(3),(sqrt(3)+0+0)/(3))=(1,(1)/(sqrt(3)))`