In $\triangle ABC$, with usual notations, if the sides $a, b$ and $c$ are in the ratio $18 : 17 : 7$, then $\cot \frac{A}{2} : \cot \frac{B}{2} : \cot \frac{C}{2} = $

The angles of a triangle are in the ratio $5:1:6$. The ratio of the smallest side to the greatest side is:

In a $\triangle ABC$,if $a^4+b^4+c^4=2b^2c^2+2a^2b^2$,then $B=$

If the angles $A, B$ and $C$ of a triangle $ABC$ are in the ratio $2:3:7$ respectively,then the sides $a, b$ and $c$ are respectively in the ratio

With usual notation in a $\Delta ABC$,if $R = k \frac{(r_1 + r_2)(r_2 + r_3)(r_3 + r_1)}{r_1 r_2 + r_2 r_3 + r_3 r_1}$,where $k$ has the value equal to:

If $p_1, p_2, p_3$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively and if $\Delta$ is the area of the triangle,$S$ is the semi-perimeter of the triangle,then find the value of $\frac{\cos A}{p_1} + \frac{\cos B}{p_2} + \frac{\cos C}{p_3}$.