In coordinate space, there are three points $\mathrm { A } , \mathrm { B } , \mathrm { C }$ not on the same line. For a plane $\alpha$ satisfying the following conditions, let $d ( \alpha )$ be the minimum distance among the distances from each point $\mathrm { A } , \mathrm { B } , \mathrm { C }$ to plane $\alpha$.\\
(a) Plane $\alpha$ intersects segment AC and also intersects segment BC.\\
(b) Plane $\alpha$ does not intersect segment AB.

Among planes $\alpha$ satisfying the above conditions, let $\beta$ be the plane where $d ( \alpha )$ is maximized. Which of the following statements in <Remarks> are correct? [4 points]

\textbf{<Remarks>}\\
$\text{ㄱ}$. Plane $\beta$ is perpendicular to the plane passing through the three points $\mathrm { A } , \mathrm { B } , \mathrm { C }$.\\
$\text{ㄴ}$. Plane $\beta$ passes through the midpoint of segment AC or the midpoint of segment BC.\\
$\text{ㄷ}$. When the three points are $\mathrm { A } ( 2,3,0 ) , \mathrm { B } ( 0,1,0 ) , \mathrm { C } ( 2 , - 1,0 )$, $d ( \beta )$ equals the distance between point B and plane $\beta$.\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ