KVPY 2016 SA Question 1

Geometry Level 3

Positive real numbers \(a\) and \(b\) are such that \(a+2b \leq 1\). Let \(A_1\) and \(A_2\) be the areas of circles with radii \(ab^3\) and \(b^2\) respectively. Find the maximum values of \(\dfrac{A_1}{A_2}\).

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