If a circle of radius `r` is touching the lines `x^2-4x y+y^2=0` in the first quadrant at points `Aa n dB` , then the area of triangle `O A B(O` being the origin) is `3sqrt(3)(r^2)/4` (b) `(sqrt(3)r^2)/4` `(3r^2)/4` (d) `r^2`

Options

A. `3sqrt(3)r^(2)//4`
B. `sqrt(3)r^(2)//4`
C. `3r^(2)//4`
D. `r^(2)`

Answer

1

Explanation

Here, `tan 2 theta =(2sqrt(4-1))/(2)=sqrt(3)`
or `theta =(pi)/(6)`
Area of `Delta OAB=(1)/(2)(r cot theta)^(2)=(1)/(2) (r sqrt(3))^(2)(sqrt(3))/(2)`