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

In an equilateral triangle $ABC$, the ratio $r : R : r_1$ is

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

$ABC$ is a triangle with $\angle A=30^{\circ}$ and $BC=10 \text{ cm}$. The area of the circumcircle of the triangle is

In $\triangle ABC$,if $a=8, b=10, c=12$,then $\frac{r}{R}=$

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