With usual notations,in triangle $ABC$,$a=\sqrt{3}+1$,$b=\sqrt{3}-1$ and $m \angle C=60^{\circ}$,then $A-B=$ (in $^{\circ}$)

The number of triangles $ABC$ that can be formed with $a = 3, b = 8$ and $\sin A = \frac{5}{13}$ is

In a triangle,the lengths of the sides are integers. Suppose that the length of one side is $1$,and the longest altitude is twice the shortest altitude. Let $R$ and $r$ be the circumradius and inradius of the triangle,respectively. If $R:r = m:n$,where $m$ and $n$ are coprime positive integers,then $m + n$ is

In a triangle,if the ex-radii $r_1, r_2, r_3$ are in the ratio $1: 2: 3$,then its sides are in the ratio

In a $\triangle ABC$,if $a \cos A = b \cos B$,where $a \neq b$,then $\triangle ABC$ is

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