In $\triangle ABC$,if $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$,then $a+c : b =$

In $\triangle ABC$,if $\cot \frac{A}{2} : \cot \frac{B}{2} : \cot \frac{C}{2} = 3 : 7 : 9$,then $a : b : c =$

If $\Delta = a^2 - (b - c)^2$,where $\Delta$ is the area of triangle $ABC$,then $\tan A$ is equal to

The smallest angle of the triangle whose sides are $6 + \sqrt{12}$,$\sqrt{48}$,and $\sqrt{24}$ is:

Assertion $(A)$: In $\triangle ABC$,if $r=6, r_2=36, R=15$,then $c^2+a^2=b^2$.
Reason $(R)$: In $\triangle ABC$,if $r:R:r_2=1:2.5:6$,then $B=90^{\circ}$.
The correct option among the following is:

In a triangle $ABC$ with usual notations,if $b \sin C(b \cos C + c \cos B) = 42$,then the area of triangle $ABC$ is: