In a $\triangle A B C, A, B$ and $C$ are in arithmetic progression, $r r_3=r_1 r_2$ and $c=10$, then $a^2+b^2+c^2=$

In a $\triangle A B C, \frac{2\left(r_1+r_3\right)}{a c(1+\cos B)}=$

In $\triangle A B C$, if $a=8, b=10, c=12$, then $\frac{r}{R}=$

In $\triangle A B C$, if $a=13, b=8, c=7$, then $\cos (B+C)=$