In $\triangle ABC$,if $a=13 \text{ cm}, b=14 \text{ cm}$ and $c=15 \text{ cm}$,then its circumradius $R$ is:

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

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

In triangle $ABC$,if $a=6, b=8$ and $c=10$,then $\frac{2 r_2 r_3}{r r_1} = $

In a $\triangle ABC$,$D, E$,and $F$ are the points of contact of the incircle with the sides $AB, BC$,and $CA$ respectively,such that $AD=\alpha, BE=\beta$,and $CF=\gamma$. Then $\frac{\alpha \beta \gamma}{\alpha+\beta+\gamma} = $