Match the items of List I with those of List II (here, $\Delta$ denotes the area of $\triangle A B C$ )

List I		List II
(A)	$$ \sum \cot A $$	(i)	$$ (a+b+c)^2 \frac{1}{4 \Delta} $$
(B)	$$ \sum \cot \frac{A}{2} $$	(ii)	$$ \left(a^2+b^2+c^2\right) \frac{1}{4 \Delta} $$
(C)	If $\tan A: \tan B: \tan C=1: 2: 3$, then $\sin A: \sin B: \sin C=$	(iii)	$$ 8: 6: 5 $$
(D)	$$ \begin{aligned} &\text { If } \cot \frac{A}{2}: \cot \frac{B}{2}: \cot \frac{C}{2}=3: 7: 9\\ &\text { then } a: b: c= \end{aligned} $$	(iv)	$$ 12: 5: 13 $$
		(v)	$$ \sqrt{5}: 2 \sqrt{2}: 3 $$
		(vi)	$$ 4 \Delta $$

$$ \text { Then, the correct match is } $$

In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\sin A: \sin B: \sin C=$

In $\triangle A B C$, if $B=90^{\circ}$, then $2(r+R)=$

In a $\triangle A B C$, if $(a-b)(s-c)=(b-c)(s-a)$, then $r_1+r_3=$