In square ABCD, let M be the midpoint of side AD. The inradii \(R\) and \(r\) of triangles \(\triangle BCM\) (incircle cEH) and \(\triangle CDM\) (incircle cFP) satisfy \(R / r = \phi\), and segment EF joining their incenters is divided by CM at K with \(|EK|/|KF| = \phi\).