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

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

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 $\triangle ABC$,if $r_1=3, r_2=10$ and $r_3=15$,then $R=$

In a triangle $ABC$, with usual notation, if $a=12, b=16, c=20$, then the ratio of the exradii of the triangle opposite to the angles in the order $\angle C, \angle B, \angle A$ is

In an equilateral triangle,the inradius $(r)$ and the circumradius $(R)$ are connected by which of the following relations?