In a triangle $ABC$,if $b = 2$ and $B = 30^\circ$,then the area of the circumcircle of triangle $ABC$ in square units is:

If $\triangle ABC$ is a right-angled isosceles triangle and $\angle C = 90^{\circ}$,then $r : r_3 =$

In a triangle $ABC$, with usual notation, if $a=12, b=16, c=20$, then the ratio of the exradii of the triangle opposite to the angles in the order $\angle C, \angle B, \angle A$ is

If $ABC$ is an isosceles triangle with base $BC$,then $rr_1=$

In $\triangle ABC$, if $a=7, b=8$ and $c=9$, then $\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=$

In a $\Delta ABC$, if $\angle C = 90^{\circ}$, $r$ and $R$ are the inradius and circumradius of the $\Delta ABC$ respectively, then $2(r+R)$ is equal to