If the angles of a triangle are in the ratio $1 : 2 : 7,$ then the ratio of its greatest side to the least side is

In $\triangle ABC$,if $a^2 \sin^2 \frac{C}{2} + c^2 \sin^2 \frac{A}{2} = \frac{b^2}{2}$,then $a+c : b =$

In a $\Delta ABC$,let $a, b$ and $c$ denote the lengths of sides opposite to vertices $A, B$ and $C$ respectively. If $b = 2, c = \sqrt{3}$ and $\angle BAC = \frac{\pi}{6}$,then the value of the circumradius of triangle $ABC$ is:

If in a $\triangle ABC$,$s(s-a) = (s-b)(s-c)$,then

In a $\triangle ABC$,if $\frac{\cos A}{a} = \frac{\cos B}{b} = \frac{\cos C}{c}$,then $\triangle ABC$ is

If the median of a $\triangle ABC$ through $A$ is perpendicular to $AC$,then $\frac{\tan A}{\tan C}=$