A circle with area \(A_1\) is contained in the interior of a larger circle with area \(A_1 + A_2\). If the radius of the larger circle is \(3\), and if \(A_1, A_2, A_1 + A_2\) is an arithmetic progression, find the radius of the smaller circle. The original answer is in the form \(\sqrt{k}\), please give the value of \(k\).

Let's think step by step and output the final answer within \boxed{}.
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