A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F, respectively. The line PQ is given by the equation `sqrt3 x+ y -6 = 0` and the point D is (3 `sqrt3/2, 3/2). Further, it is given that the origin and the centre of C are on the same side of the line PQ. The equation of circle C is

Options

A. `y=(2)/(sqrt3)x+1, y= - (2)/(sqrt3)x-1`
B. `y=(1)/(sqrt3)x ,y=0`
C. `y=(sqrt3)/(2)x+1, y= - (sqrt3)/(2)x-1`
D. `y=sqrt3x ,y=0`

Answer

A

Explanation

Equation of `QR, RP "are" y=(2)/(sqrt3)x+1and y=-(2)/(sqrt3) x-1`.