In an equilateral triangle of side $2\sqrt{3} \text{ cm}$,the circum-radius is ..... $\text{cm}$.

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

The circumradius of triangle $PRS$ is . . . . .

If $I$ is the incentre of $\triangle ABC$ and $P_1, P_2, P_3$ are respectively the radii of the circumcircles of the $\triangle IBC, \triangle ICA$ and $\triangle IAB$,then $P_1 P_2 P_3=$

If the vertices of a triangle are $A(0, -6)$,$B(-6, 0)$,and $C(1, 1)$,find the coordinates of the excenter opposite to vertex $A$.

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