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

If the angles $A, B$ and $C$ of a triangle are in $A.P.$ and if $a, b$ and $c$ denote the length of the sides opposite to $A, B$ and $C$ respectively,then the value of $\frac{a}{b} \sin 2B + \frac{b}{a} \sin 2A$ is

In any triangle $ABC$, if $a: b: c = 2: 3: 4$, then $R: r =$

In a $\triangle ABC$,$\angle C = 60^{\circ}$ and $\angle A = 75^{\circ}$. If $D$ is a point on $AC$ such that the area of $\triangle BAD$ is $\sqrt{3}$ times the area of $\triangle BCD$,then the measure of $\angle ABD$ is (in $^{\circ}$)

In a $\triangle ABC$,if $r_1 = 2r_2 = 3r_3$,then the ratio $a : b$ is:

In a $\triangle ABC$,if $r_1 = 2r_2 = 3r_3$,then $a : b =$