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. (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. `y=(2)/(sqrt(3))x+1,y= -(2)/(sqrt(2))x-1`
B. `y=(1)/(sqrt(3))x,y=0`
C. `y=(sqrt(3))/(2)x+1,y=- (sqrt(3))/(2)x-1`
D. `y=sqrt(3)x,y=0`

Answer

4

Explanation

Equation of line PR which is parallel to DE and passes through F is `(y-0) = 0 ( x-sqrt(3)) implies y=0`.
Similarly equation of line QR which is parallel to DF and passes through the point E is
`(y-(3)/(2))=(((3)/(2)-0)/((3sqrt(3))/(2)-sqrt(3)))(x-(sqrt(3))/(2))`.
`implies y = sqrt(3) x`