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

Question

$(a)\;b^2=ac\qquad(b)\;2b=a+c\qquad(c)\;2ac=b(a+c)\qquad(d)\;a+b=c$