The circle C_1: x^2+y^2=3, with centre at O, the parabola x^2=2 y at the pointin the first quadra...

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The circle C_1: x^2+y^2=3, with centre at O, the parabola x^2=2 y at the pointin 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 โˆš(3) and centres Q_2 and Q_3, respectively. If Q_2 and Q_3 lie on the y-axis, then
(A) Q_2Q_3=12
(B) R_2R_3=4 โˆš(6)
(C) area of the triangle OR_2R_3 is 6 โˆš(2)
(D) area of the triangle PQ_2Q_3 is 4 โˆš(2)
[JEE Adv. 2016, 4]

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