The circle $C_1: x^2 + y^2 = 3$, with centre at $O$, intersects the parabola $x^2 = 2y$ at the point $P$ in the first quadrant. Let the tangent to the circle $C_1$ at $P$ touches other two circles $C_2$ and $C_3$ at $R_2$ and $R_3$, respectively. Suppose $C_2$ and $C_3$ have equal radii $2\sqrt{3}$ and centres $Q_2$ and $Q_3$, respectively. If $Q_2$ and $Q_3$ lie on the $y$-axis, then (A) $Q_2 Q_3 = 12$ (B) $R_2 R_3 = 4\sqrt{6}$ (C) area of the triangle $OR_2R_3$ is $6\sqrt{2}$ (D) area of the triangle $PQ_2Q_3$ is $4\sqrt{2}$
The circle $C_1: x^2 + y^2 = 3$, with centre at $O$, intersects the parabola $x^2 = 2y$ at the point $P$ in the first quadrant. Let the tangent to the circle $C_1$ at $P$ touches other two circles $C_2$ and $C_3$ at $R_2$ and $R_3$, respectively. Suppose $C_2$ and $C_3$ have equal radii $2\sqrt{3}$ and centres $Q_2$ and $Q_3$, respectively. If $Q_2$ and $Q_3$ lie on the $y$-axis, then\\
(A) $Q_2 Q_3 = 12$\\
(B) $R_2 R_3 = 4\sqrt{6}$\\
(C) area of the triangle $OR_2R_3$ is $6\sqrt{2}$\\
(D) area of the triangle $PQ_2Q_3$ is $4\sqrt{2}$