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The circle \( C_{1}=x^{2}+y^{2}=3 \), with centre at \( O \),
\( \mathrm{P} \) intersects the parabola \( x^{2}=2 y \) at the point \( P \) in the

W 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 \( Q \), lie on the \( y \)-axis, then
(1) \( Q_{2} Q_{3}=12 \)
(2) \( R_{2} R_{3}=4 \sqrt{6} \)
(3) Area of the triangle \( \mathrm{OR}_{2} R_{3} \) is \( 6 \sqrt{2} \)
(4) Area of the triangle \( P Q_{2} Q_{3} \) is \( 4 \sqrt{2} \)
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