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 `((3sqrt3)/2, 3/2)`. Further, it is given that the origin and the centre of C are on the same side of the line PQ. (1)The equation of circle C is (2)Points E and F are given by (3)Equation of the sides QR, RP are

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. `((sqrt( 3))/( 2) , ( 3)/( 2)), ( sqrt( 3) , 0)`
B. `((sqrt( 3))/( 2) , ( 1)/( 2)), ( sqrt( 3) , 0)`
C. `((sqrt( 3))/( 2) , ( 3)/( 2)), ( (sqrt( 3))/(2),(1)/(2))`
D. `( ( 3)/( 2),(sqrt( 3))/( 2) ), ( (sqrt( 3))/(2),(1)/(2))`

Answer

A