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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 $$\sqrt{3}x + y - 6 = 0$$ 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 PQ.
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