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The incentre of the triangle with vertic...

The incentre of the triangle with vertices (1, `sqrt3`) (0,0) (2,0) is

A

`(1,(sqrt(3))/(2))`

B

`((2)/(3),(1)/(sqrt(3)))`

C

`((2)/(3),(sqrt(3))/(2))`

D

`(1,(1)/(sqrt(3)))`

Text Solution

Verified by Experts

Let the vertices of triangle be `A(1,sqrt(3))`, `B(0,0)` and `C(2,0)`. Here , `AB=BC=CA=2`.
Therefore it is an equilateral triangle . So, the incentre coincides with centroid.
`:. I-=((0+1+2)/(3),(0+0+sqrt(3))/(3))`
`I-=(1,1//sqrt(3))`
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