JEE Advance - Mathematics (1994 - No. 1)
The circle $${x^2} + {y^2} = 1$$ cuts the $$x$$-axis at $$P$$ and $$Q$$. Another circle with centre at $$Q$$ and variable radius intersects the first circle at $$R$$ above the $$x$$-axis and the line segment $$PQ$$ at $$S$$. Find the maximum area of the triangle $$QSR$$.
$$\frac{\sqrt{3}}{4}$$ sq. units
$$\frac{3\sqrt{3}}{8}$$ sq. units
$$\frac{\sqrt{3}}{2}$$ sq. units
$$\frac{4\sqrt{3}}{9}$$ sq. units
$$\frac{\sqrt{3}}{3}$$ sq. units