The circle `C_(1) : x^(2)+y6(2)=3`, with cenre 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 `2sqrt(3)` and centres `Q_(2)` and `Q_(3)` respectively. If `Q_(2)` and `Q_(3)` lie on the y-axis, then `Q_(2)Q_(3)=`

Options

A. `Q_(2)Q_(3)=12`
B. `R_(2)R_(3)=4sqrt6`
C. area of the triangle `OR_(2)R_(3)` is `6sqrt2`
D. area of the triangle `PQ_(2)Q_(3)` is `4sqrt2`

Answer

A, B, C