Question

The minimum value of r, for which the line arg $\left(z\right)=\frac{\pi }{6}$ and the circle $|z-2\sqrt{3}i|=r$ intersect, is

• A. $4\sqrt{3}$
• B. $3\sqrt{3}$
• C. 3
• D. 6

Answer 1

The correct option is C 3

$arg\left(z\right)=\frac{\pi }{6}$ is the line $x-\sqrt{3}y=0,$ and $|z-2\sqrt{3i}|=r$ is the circle with centre $(0,2\sqrt{3})$ and radius r now they will intersect if perpendicular distance of the centre form the line is $\le$ r
i.e. $3\le r$
i.e. $r\ge 3$