IIT-JEE 2008 · Paper 1, Mathematics question 17

Paragraph for Question Nos. 15 to 17

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 $\sqrt3x+y-6=0$ and the point $D$ is $\left(\frac{3\sqrt3}2,\frac32\right)$. Further, it is given that the origin and the centre of $C$ are on the same side of the line $PQ$.