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 and D, E, F` respectively. The line `PQ` is given by the equation `sqrt(3) +y-6=0` and the point `D` is `((sqrt(3))/(2), 3/2)`. Equation of the sides `QR, RP` are : (A) `y=2/sqrt(3) x + 1, y = 2/sqrt(3) 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`

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 and D, E, F respectively. The line PQ is given by the equation sqrt(3) +y-6=0 and the point D is ((sqrt(3))/(2), 3/2) The equation of circle C is : (A) (x-2sqrt(3))^2 + (y-1)^2 = 1 (B) (x-2sqrt(3))^2 + (y+1/2)^2 = 1 (C) (x-sqrt(3))^2 + (y+1)^2 = 1 (D) (x-sqrt(3))^2 + (y-1)^2 =1

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 and D, E, F respectively. The line PQ is given by the equation sqrt(3) +y-6=0 and the point D is ((sqrt(3))/(2), 3/2) . Point E and F are given by : (A) (sqrt(3)/2, 3/2), (sqrt(3), 0) (B) (sqrt(3)/2, 3/2), (sqrt(3)/2, 1/2) (C) (3/2, sqrt(3)/2), (sqrt(3)/2, 1/2)

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

The equations y= +-sqrt3 x,y =1 are the sides of

A vertex of an equilateral triangle is at (2, 3), and th equation of the opposite side is x+y=2 , then the equaiton of the other two sides are (A) y=(2+sqrt(3)) (x-2), y-3=2sqrt(3)(x-2) (B) y-3=(2+sqrt(3) (x-2), y-3= (2-sqrt(3) (x-2) (C) y+3=(2-sqrt(3)(x-2), y-3=(2-sqrt(3) (x+2) (D) none of these

Number of equilateral triangle with y=sqrt3(x-1)+2;y=- sqrt3x as two of its sides is

The lines represented by the equation x^2 + 2sqrt(3)xy + 3y^(2) -3x -3sqrt(3)y -4=0 , are