In a $\triangle ABC$, $\frac{\Delta^2}{a^2+b^2+c^2}\left(\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}+\frac{1}{r^2}\right) = $

The perimeter of $\triangle ABC$ is $36 \text{ cm}$ and its inradius is $8 \text{ cm}$. Then,the area of the triangle is (in $\text{ cm}^2$)

Let $ABC$ be an equilateral triangle with side length $a$. Let $R$ and $r$ denote the radii of the circumcircle and the incircle of triangle $ABC$ respectively. Then,as a function of $a$,the ratio $\frac{R}{r}$

If the sides of a triangle are $13, 14, 15$,then the radius of its incircle is

In $\triangle ABC$, if $a:b:c = 4:5:6$, then the ratio of the circumradius to its inradius is

In a $\triangle ABC$, $r_1, r_2$ and $r_3$ respectively denote the radii of the excircles opposite to the vertices $A, B, C$ and $r$ denotes the radius of the incircle. If $p_1, p_2$ and $p_3$ respectively are the altitudes of the triangle from the vertices $A, B$ and $C$, then $\left(\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}\right)^2$ is equal to