In any $\triangle A B C, r^2 \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2}=$

In $\triangle A B C$, if $A$ is acute, $C$ is obtuse, $\sin A=\frac{3 \sqrt{3}}{14}, a=3$ and $b=5$, then $c=$

If $\Delta$ denotes the area of $\triangle A B C$, then $(b \sin C+c \sin B)(b \cos C+c \cos B)=$

Let $A$ be the area of in-circle and $A_1, A_2, A_3$ be the area of ex-circles of a triangle. If $A_1=4, A_2=9, A_3=16$, then $A=$