If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

With usual notations,if triangle $ABC$ is right-angled at $C$,then $\left(\frac{a^{2}+b^{2}}{a^{2}-b^{2}}\right) \sin (A-B) =$

In a triangle $ABC$ with usual notations,if $3a = b + c$,then $\cot \frac{B}{2} \cdot \cot \frac{C}{2} =$

In any $\triangle ABC$, $r_1 r_2 + r_2 r_3 + r_3 r_1$ is equal to

In a triangle $ABC$,$m \angle A, m \angle B, m \angle C$ are in $A$.$P$. and the lengths of the two larger sides are $10$ units and $9$ units respectively. Then the length (in units) of the third side is:

In $\Delta ABC,$ if $a = 16, b = 24$ and $c = 20,$ then $\cos \frac{B}{2} = $