In triangle $ABC$, if $a=7, b=10, c=11$, then $\frac{R}{r}=$

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

If the sides of a triangle are $13, 14, 15$,then the radius of its incircle is

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

Let $ABC$ be a scalene triangle with incentre $I$ and circumcentre $O$. Suppose $B, C, I, O$ are concyclic points. Then $\angle B + \angle C$ is (in $^{\circ}$)

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} = $