Properties Of Triangles

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

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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)	\( 4 \Delta \)

\(\text { Then, the correct match is }\)