Suppose $$\triangle A B C$$ is an isosceles triangle with $$\angle C=90^{\circ}, A=(2,3)$$ and $$B=(4,5)$$. Then, the centroid of the triangle is

In a $$\triangle A B C$$, if $$a \neq b, \frac{a \cos A-b \cos B}{a \cos B-b \cos A}+\cos C=$$

If in a $$\triangle A B C, a=2, b=3$$ and $$c=4$$, then $$\tan (A / 2)=$$

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