A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (–1, 1) and (2, 3). Then the centroid of this triangle is :

The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : $$\sqrt 3 $$. If c = 4 cm, then the area (in sq. cm) of this triangle is :

If the lengths of the sides of a triangle are in A.P. and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is :

Given $${{b + c} \over {11}} = {{c + a} \over {12}} = {{a + b} \over {13}}$$ for a $$\Delta $$ABC with usual notation.

If   $${{\cos A} \over \alpha } = {{\cos B} \over \beta } = {{\cos C} \over \gamma },$$ then the ordered triad ($$\alpha $$, $$\beta $$, $$\gamma $$) has a value :