In a $\triangle A B C$, if $c^2-a^2=b(\sqrt{3} c-b)$ and $b^2-a^2=c(c-a)$ then, $\angle A B C$

Let $A B C$ be a triangle right angled at $B$. If $a=13$ and $c=84$, then $r+R=$

In a $\triangle A B C$, if $r_1=4, r_2=8$ and $r_3=24$, then $a: b: c=$

In a $\triangle A B C,\left(r_2+r_3\right) \operatorname{cosec}^2\left(\frac{A}{2}\right)=$