If, in a $\Delta \; ABC, \tan \large\frac{A}{2}=\frac{5}{6}$ and $\tan \large\frac{C}{2}=\frac{2}{5},$ then $a,b,c$ are such that:

Question

\[\begin {array} {1 1} (a)\;b^2=ac & \quad (b)\;2b=a+c \\ (c)\;2ac=b(a+c) & \quad (d)\;a+b=c \end {array}\]