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) . 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) . 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

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

The vertex P of an equilateral triangle /_PQR is at (2,3) and the equation of the opposite side QR is given by x+y=2. Find the possible equations of the side PQ.

The equation of the base of an equilateral triangle ABC is x+y=2 and the vertex is (2,-1). The area of the triangle ABC is: (sqrt(2))/(6) (b) (sqrt(3))/(6) (c) (sqrt(3))/(8) (d) None of these