61. Exemplar exercise problems XXVI

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 \(m\).