In an acute angled triangle,$\cot B \cot C + \cot A \cot C + \cot A \cot B$ is equal to

In triangle $ABC$,$(b + c)\cos A + (c + a)\cos B + (a + b)\cos C = $

The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the values of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$

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

In $\triangle ABC$,the sum of the lengths of two sides is $x$ and the product of those lengths is $y$. If $c$ is the length of the third side and $x^2 - c^2 = y$,then the circumradius of the triangle is

In $\triangle ABC$,with usual notations,if $\cos A = \frac{\sin B}{\sin C}$,then the triangle is $......$