Consider the circle $\mathrm{x}^2+\mathrm{y}^2=9$ and the parabola $\mathrm{y}^2=8 \mathrm{x}$. They intersect at $\mathrm{P}$ and $\mathrm{Q}$ in the first and the fourth quadrants, respectively. Tangents to the circle at $\mathrm{P}$ and $\mathrm{Q}$ intersect the $\mathrm{x}$-axis at $\mathrm{R}$ and tangents to the parabola at $\mathrm{P}$ and $\mathrm{Q}$ intersect the $\mathrm{x}$-axis at $\mathrm{S}$.
$1.$ The ratio of the areas of the triangles $P Q S$ and $P Q R$ is
$(A)$ $1: \sqrt{2}$ $(B)$ $1: 2$ $(C)$ $1: 4$ $(D)$ $1: 8$
$2.$ The radius of the circumcircle of the triangle PRS is
$(A)$ $5$ $(B)$ $3 \sqrt{3}$ $(C)$ $3 \sqrt{2}$ $(D)$ $2 \sqrt{3}$
$3.$ The radius of the incircle of the triangle $P Q R$ is
$(A)$ $4$ $(B)$ $3$ $(C)$ $8 / 3$ $(D)$ $2$
Give the answer question $1,2$ and $3.$