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

If the angular bisector of the angle $A$ of the triangle $ABC$ meets its circumcircle at $E$ and the opposite side $BC$ at $D$, then $DE \cos \frac{A}{2} = $

In a triangle $ABC$,if $r r_2 = r_1 r_3$,then $\cos 2B =$

In $\triangle ABC$,find the value of $\frac{r_1-r}{a}+\frac{r_2-r}{b}$.

In $\triangle ABC$,if $r=1, R=4$ and $\Delta=8$,then $\frac{1}{ab}+\frac{1}{bc}+\frac{1}{ca}=$

In $\triangle ABC$,if $r$ is the inradius and $r_1, r_2, r_3$ are the ex-radii,then $\frac{1}{4}[b^2 \sin 2C + c^2 \sin 2B] =$