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

In a $\Delta ABC$,if two sides $b$ and $c$ and an angle $B$ are given.
Statement $-1$: Let $b = 5 \ cm, c = 3 \ cm$ and $\angle B = 60^\circ$. The total number of possible triangles is $2$.
Statement $-2$: If $c \sin B < b < c$ and $B$ is an acute angle,then there are two possible values of $\angle C$.

In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ equals:

In a triangle $ABC$, if $r_1=4, r_2=8$ and $r_3=24$, then $a: b: c=$

If in a triangle $ABC$ the sides $AB$ and $AC$ are perpendicular,then the true equation is

If in triangle $ABC$,$\cos A = \frac{\sin B}{2\sin C}$,then the triangle is