In $\triangle ABC$,if $r_1: r_2 = 7: 8$ and $r_1: r_3 = 3: 4$,then $a: b: c =$

In a $\Delta ABC$,if $\angle C = 30^\circ$,$a = 47 \text{ cm}$ and $b = 94 \text{ cm}$,then the triangle is

In any triangle $ABC$, $r^2 \cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} =$

If the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one,then the area (in sq. units) of that triangle is

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 $\frac{\cos A}{p_1} + \frac{\cos B}{p_2} + \frac{\cos C}{p_3}$.

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