In $\triangle A B C$, if $a: b: c=4: 5: 6$, then the ratio of the circumradius to its inradius is

The perimeter of a $\triangle A B C$ is 6 times the arithmetic mean of the values of the sine of its angles. If its side $B C$ is of unit length, then $\angle A=$

In $\triangle A B C$, if $b=6, c=7$ and $\tan \frac{A}{2}=\frac{1}{\sqrt{6}}$, then the inradius of $\triangle A B C$ is

In $\triangle A B C$, if $a=7, b=8$ and $c=9$, then $\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=$