[BD] is a median of \( \triangle ABC \). \( m(\widehat{ABD}) = 90^\circ \), \(|AB| = 2\), and \(|AC| = 6\). Find the length of \(|BC|\). The original answer is in the form of \(k\sqrt{m}\). Please give the value of \(k + m\).

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