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 $\angle A=$

In $\triangle ABC$,$a=6 \text{ cm}$,$b=10 \text{ cm}$ and $c=14 \text{ cm}$. Then,the sum of the acute angles of the triangle is (in $^{\circ}$)

Let $f, g, h$ be the lengths of the perpendiculars from the circumcentre of the $\Delta ABC$ on the sides $a, b$ and $c$ respectively. If $\frac{a}{f} + \frac{b}{g} + \frac{c}{h} = \lambda \frac{abc}{fgh}$,then the value of $\lambda$ is:

In triangle $ABC$,if $\frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c}$,then the triangle is:

In a triangle $ABC$ with usual notations,if $\cot \frac{A}{2} = \frac{b+c}{a}$,then the triangle $ABC$ is

In a $\triangle ABC$,if $\tan(A/2)$,$\tan(B/2)$,and $\tan(C/2)$ are in Arithmetic Progression,then which of the following options is always correct?