$\frac{a\cos A + b\cos B + c\cos C}{a + b + c} = $

If angles $A, B$ and $C$ are in $A$.$P$.,then $\frac{a+c}{b}$ is equal to

If the area of triangle $ABC$ is $b^2-(c-a)^2$,then $\tan B=$

If in the $\Delta ABC$,$AB = 2BC$,then find the ratio $\tan \frac{B}{2} : \cot \left( \frac{C - A}{2} \right)$.

Consider a triangle $ABC$ and let $a, b$ and $c$ denote the lengths of the sides opposite to vertices $A, B$ and $C$ respectively. Suppose $a=6, b=10$ and the area of the triangle is $15 \sqrt{3}$. If $\angle ACB$ is obtuse and if $r$ denotes the radius of the incircle of the triangle,then $r^2$ is equal to

In a $\triangle ABC$,if $a+c=5b$,then $\cot \frac{A}{2} \cot \frac{C}{2}$ is equal to