In $\triangle A B C$, if $(a+c)^2=b^2+3 c a$, then $\frac{a+c}{2 R}=$

In $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression $\Delta=\frac{\sqrt{3}}{2}$ and $r_1 r_2=r_2 r$, then $R=$

If 7 and 8 are the length of two sides of a triangle and $a^{\prime}$ is the length of its smallest side. The angles of the triangle are in AP and ' $a$ ' has two values $a_1$ and $a_2$ satisfying this condition. If $a_1 < a_2$, then $2 a_1+3 a_2=$

In $\triangle A B C$, if $a=13, b=14$ and $\cos \frac{C}{2}=\frac{3}{\sqrt{13}}$, then $2 r_1=$