KVPY 2016 SA Question 1

Geometry Level 2

Positive real numbers aa and bb are such that a+2b1a+2b \leq 1. Let A1A_1 and A2A_2 be the areas of circles with radii ab3ab^3 and b2b^2 respectively. Find the maximum values of A1A2\dfrac{A_1}{A_2}.


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