In a $\triangle ABC$,if $r_1=12, r_2=18$ and $r_3=36$,then $b=$

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:

If $a, b, c$ are the sides of a triangle $ABC,$ then which of the following inequalities is not true?

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 $\triangle ABC$,if $a, b, c$ are its sides and $\angle C = 60^{\circ}$,find the value of $\frac{a}{b+c} + \frac{b}{c+a}$.

In $\triangle ABC$,$(\cot A+\cot B)(\cot B+\cot C)(\cot C+\cot A) =$