A circle $C$ of radius 1 is inscribed in an equilateral triangle $P Q R$. The points of contact of $C$ with the sides $P Q , Q R , R P$ are $D , E , F$, respectively. The line $P Q$ is given by the equation $\sqrt { 3 } x + y - 6 = 0$ and the point $D$ is $\left( \frac { 3 \sqrt { 3 } } { 2 } , \frac { 3 } { 2 } \right)$. Further, it is given that the origin and the centre of $C$ are on the same side of the line $P Q$. The equation of circle $C$ is (A) $\quad ( x - 2 \sqrt { 3 } ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$ (B) $( x - 2 \sqrt { 3 } ) ^ { 2 } + \left( y + \frac { 1 } { 2 } \right) ^ { 2 } = 1$ (C) $\quad ( x - \sqrt { 3 } ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 1$ (D) $( x - \sqrt { 3 } ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$
A circle $C$ of radius 1 is inscribed in an equilateral triangle $P Q R$. The points of contact of $C$ with the sides $P Q , Q R , R P$ are $D , E , F$, respectively. The line $P Q$ is given by the equation $\sqrt { 3 } x + y - 6 = 0$ and the point $D$ is $\left( \frac { 3 \sqrt { 3 } } { 2 } , \frac { 3 } { 2 } \right)$. Further, it is given that the origin and the centre of $C$ are on the same side of the line $P Q$.
The equation of circle $C$ is\\
(A) $\quad ( x - 2 \sqrt { 3 } ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$\\
(B) $( x - 2 \sqrt { 3 } ) ^ { 2 } + \left( y + \frac { 1 } { 2 } \right) ^ { 2 } = 1$\\
(C) $\quad ( x - \sqrt { 3 } ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 1$\\
(D) $( x - \sqrt { 3 } ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$