If the pair of straight lines `x ysqrt(3)-x^2=0` is tangent to the circle at `Pa n dQ` from the origin `O` such that the area of the smaller sector formed by `C Pa n dC Q` is `3pis qdotu n i t ,` where `C` is the center of the circle, the `O P` equals (a)`((3sqrt(3)))/2` (b) `3sqrt(3)` (c) 3 (d) `sqrt(3)`

Options

A. `(3 sqrt(3))//2`
B. `3 sqrt(3)`
C. 3
D. `sqrt(3)`

Answer

2

Explanation

`tan 30^(@)=(r )/(OP)`
or `OP =r sqrt(3)`
Also, `r^(2)(1)/(2) (2pi)/(3)=3pi`
`:. r=3`
`:. OP=3sqrt(3)`