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 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 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

(2+sqrt(3))/(2-sqrt(3))+(2-sqrt(3))/(2+sqrt(3))+(sqrt(3)+1)/(sqrt(3)-1)is

sqrt((4)/(3))-sqrt((3)/(4))=?(4sqrt(3))/(6) (b) (1)/(2sqrt(3))(c)1(d)-(1)/(2sqrt(3))

The value of (2 + sqrt(3))/(2- sqrt(3)) + (2- sqrt(3))/(2 + sqrt(3)) + ( sqrt(3) + 1)/(sqrt(3) -1) is

If a=(sqrt(3))/(2), then sqrt(1+a)+sqrt(1-a)=?(2-sqrt(3))(b)(2+sqrt(3))(c)((sqrt(3))/(2))(d)sqrt(3)