In $\triangle ABC$,if $2R + r = r_2$,then $\angle B$ is equal to

In a $\triangle ABC$,which of the following formulae are correct?
$I. r = 4R \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$
$II. r_1 = (s-a) \tan \frac{A}{2}$
$III. r_3 = \frac{\Delta}{s-c}$

In $\Delta ABC,$ if $b = 6, c = 8$ and $\angle A = 90^\circ,$ then the circumradius $R$ is:

If the roots of the equation $x^3-11x^2+36x-36=0$ are the ex-radii of a triangle $ABC$, then the perimeter of the triangle $ABC$ is

In a triangle $ABC$,if $r_1=3, r_2=4, r_3=6$,then $b=$

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