Geometry Level 5

Two sides of a quadrilateral have length $$a$$, while the other two are of length $$b$$. Let the maximum possible area of the quadrilateral be $$A$$.

Let the area of an ellipse with the major and minor axes as $$a$$ and $$b$$, be $$B$$.

Then the value of $$\frac{B}{A}$$ is ...

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