A straight line cuts off the intercepts $$\mathrm{OA}=\mathrm{a}$$ and $$\mathrm{OB}=\mathrm{b}$$ on the positive directions of $$x$$-axis and $$y$$ axis respectively. If the perpendicular from origin $$O$$ to this line makes an angle of $$\frac{\pi}{6}$$ with positive direction of $$y$$-axis and the area of $$\triangle \mathrm{OAB}$$ is $$\frac{98}{3} \sqrt{3}$$, then $$\mathrm{a}^{2}-\mathrm{b}^{2}$$ is equal to :

The lengths of the sides of a triangle are 10 + x², 10 + x² and 20 $$-$$ 2x². If for x = k, the area of the triangle is maximum, then 3k² is equal to :

Let a, b and c be the length of sides of a triangle ABC such that $${{a + b} \over 7} = {{b + c} \over 8} = {{c + a} \over 9}$$. If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of $${R \over r}$$ is equal to :