In $\triangle A B C$, if $a, b, c$ are in arithmetic progression and $A=2 C$, then $b: c=$

Assertion (A) In $\triangle A B C$, if $r=6, r_2=36, R=15$, then $c^2+a^2=b^2$.

Reason (R) In $\triangle A B C$, if $r: R: r_2=1: 2.5: 6$, then $B=90^{\circ}$. The correct option among the following is

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 $\angle A=$