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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 \(P Q\).Question:
The equation of circle \(C\) is

1. A
   \((x-2 \sqrt{3})^2+(y-1)^2=1\)
   
2. B
   \((x-2 \sqrt{3})^2+\left(y+\frac{1}{2}\right)^2=1\)
   
3. C
   \((x-\sqrt{3})^2+(y+1)^2=1\)
   
4. D
   \((x-\sqrt{3})^2+(y-1)^2=1\)