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

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

The inradius of a circle inscribed in an isosceles right-angled triangle,where one of the angles is $\frac{\pi}{2}$,is $1$. Find the area of the triangle (in sq. units).

In $\triangle ABC$,suppose the radius of the excircle opposite to angle $A$ is denoted by $r_1$,similarly $r_2$ for angle $B$,and $r_3$ for angle $C$. If $r_1=2, r_2=3, r_3=6$,then what is $(a, b, c)$?

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

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 $A$.