If the angles of a $$\triangle A B C$$ are in the ratio $$1: 2: 3$$, then the corresponding sides are in the ratio

In a $$\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+r_3 \cot \frac{C}{2}=$$

In $$\triangle A B C$$, medians $$A D$$ and $$B E$$ are drawn. If $$A D=4, \angle D A B=\frac{\pi}{6}$$ and $$\angle A B E=\frac{\pi}{3}$$, then the area of $$\triangle A B C$$ is

In a $$\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$$, then the triangle is