In a triangle $ABC$,$a : b : c = 4 : 5 : 6$. The ratio of the radius of the circumcircle to that of the incircle is

Let $A$ be the area of the in-circle and $A_1, A_2, A_3$ be the areas of the ex-circles of a triangle. If $A_1=4, A_2=9, A_3=16$, then $A=$

Let $ABC$ be a triangle right-angled at $B$. If $a = 13$ and $c = 84$, then $r + R = $

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 $\triangle ABC$, $r_1, r_2$ 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 $\Delta ABC,$ if $b = 6, c = 8$ and $\angle A = 90^\circ,$ then the circumradius $R$ is: