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 $r$ is the radius of the inscribed circle,then what is the value of $\frac{ab - r_1 r_2}{r_3}$?

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 a $\triangle ABC$,let $a, b, c, s, r, R, I, S, r_1, r_2, r_3$ stand for their usual meanings. Match the items of List-$I$ with those of List-$II$.

List-$I$	List-$II$
$A. \tan \frac{A}{2} = \frac{r}{s-a}$	$I. (AI) \left( \frac{\sqrt{(s-b)(s-c)}}{bc} \right)$
$B. r$	$II. R^2$
$C. (SI)^2 + 2Rr$	$III. (4R + r + \sqrt{2}s)(4R + r - \sqrt{2}s)$
$D. r_1^2 + r_2^2 + r_3^2$	$IV. \frac{Rr}{S}$
	$V. \frac{(s-b)(s-c)}{\Delta}$

The correct match is:

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

In a $\triangle ABC$,$r_1, r_2$ and $r_3$ respectively denote the radii of the excircles opposite to the vertices $A, B, C$ and $r$ denotes the radius of the incircle. If $p_1, p_2$ and $p_3$ respectively are the altitudes of the triangle from the vertices $A, B$ and $C$,then $\left(\frac{1}{p_1}+\frac{1}{p_2}+\frac{1}{p_3}\right)^2$ is equal to

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