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Two lines \(l\) and \(m\) intersect at the point \(O\) and \(P\) is a point on a line \(n\) passing through the point \(O\) such that \(P\) is equidistant from \(l\) and \(m\). Prove that \(n\) is the bisector of the angle formed by \(l\) and \(m\).
 
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