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

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`

Options

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

Answer

D