The inradius of the triangle whose sides are $3, 5, 6$ is

In $\triangle ABC$,if $\frac{1}{a+b} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $\sin A$ is equal to

In a $\triangle ABC$,if $b=2, c=3$ and $\angle B=\frac{\pi}{6}$,then $a$ satisfies the equation

In a triangle $ABC$,with usual notations,if $a=5$,$b=7$,and $\sin A=\frac{3}{4}$,then the total number of triangles possible is:

Let $ABC$ be an acute-angled triangle with area $R$. Then,$\sqrt{a^2 b^2-4 R^2}+\sqrt{b^2 c^2-4 R^2}+\sqrt{c^2 a^2-4 R^2} = $

In $\Delta ABC$,$8 \Delta = (b + c)(bc + 1)$,then the circumradius of $\Delta ABC$ is (where $\Delta$ denotes the area of the triangle and $b, c$ are the lengths of sides $AC$ and $AB$ respectively):