In a $\triangle ABC$,if $a: b: c = 4: 5: 6$,then the ratio of the radius of its circumcircle to that of its incircle is:

The radius of the incircle of a triangle with sides $18 \, cm$,$24 \, cm$,and $30 \, cm$ is ..... $cm$.

In $\triangle ABC$,with usual notation,observe the two statements given below :
$(I)$ $r r_1 r_2 r_3 = \Delta^2$
$(II)$ $r_1 r_2 + r_2 r_3 + r_3 r_1 = s^2$
Which of the following is correct?

In $\triangle ABC$,if $r_1=3, r_2=10$ and $r_3=15$,then $R=$

In a $\triangle ABC$,$2A + C = 300^{\circ}$. If the circumradius $R$ of the $\triangle ABC$ is eight times its inradius $r$,then $\sin \frac{C}{2} = $

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