There are 3 common tangent of the parabola $y^2=4x$  and the circle $x^2+y^2-6x=0$  forming a triangle T. Which of the following is/are true about the triangle T.

$$\begin{gathered} y=mx+\frac{1}{m}\Rightarrow m^{2}x-my+1=0 \\ p=r\Rightarrow \left|\frac{3m^2+1}{\sqrt{m^4+m^2}}\right|=3 \\ 9m^4+6m^2+1=9m^4+9m^2 \\ m=\infty ,\frac{1}{\sqrt{3}},\frac{-1}{\sqrt{3}} \\ \text{ lines are }x=0, \\ y=\frac{1}{\sqrt{3}}x+\sqrt{3},y=-\frac{1}{\sqrt{3}}x-\sqrt{3} \end{gathered}$$

$\Delta ABC$  is an equilateral triangle with side  $=2\sqrt{3}$