A triangle \( \triangle ABC \) is inscribed in a circle with center \(O\) and radius \( r \). The coordinates of points \(A\), \(B\), and \(C\) are \((1, 0)\), \((5, 0)\), and \((3, 4)\) respectively. Find the radius \( r \) of the circumscribed circle. Let's think step by step and output the final answer within \boxed{}.
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