Fig. $1$

$2.$ Two coils, with terminals $AB$ and $CD$ respectively, are inductively coupled. The inductance measured between the terminals $AB$ is $380$ uH and that between terminals $CD$ is $640$ uH $.$ With $B$ joined to $C,$ the inductance measured between the terminals $AD$ is $1600$ uH $.$ Calculate : $($a$)$ the mutual inductance of the coils and $($b$)$ the inductance between terminals AC when B is connected to D $.$