Points \(A\) and \(B\) are on a circle of radius \(5\) and \(AB = 6\). Point \(C\) is the midpoint of the minor arc \(AB\). What is the length of the line segment \(AC\)? The answer is in the form \(\sqrt{k}\). Please find the value of \(k\).

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