In a $\triangle ABC$,if $a=26, b=30$,and $\cos C=\frac{63}{65}$,then $c=$

Assertion $(A)$: In $\triangle ABC$,if $r=6, r_2=36, R=15$,then $c^2+a^2=b^2$.
Reason $(R)$: In $\triangle ABC$,if $r:R:r_2=1:2.5:6$,then $B=90^{\circ}$.
The correct option among the following is:

In a $\triangle ABC$,if $a+3b=3c$,then $\sin \frac{A}{2} =$

In a triangle $ABC$,with usual notations,if $m \angle A = 60^{\circ}$,$b = 8$,$a = 6$,and $B = \sin^{-1} x$,then $x$ has the value:

In a triangle $ABC$,$a = 4$,$b = 3$,and $\angle A = 60^\circ$. Then $c$ is the root of the equation:

In a $\triangle ABC$,if $a=5, b=6, c=7$,then the length of the median drawn from $B$ is