A comparison of lengths
Let \(AD,BE,CF\) be altitudes of an acute triangle \(ABC\) with \( AB > AC\). Line \(EF \) meets \(BC\) at \(P\), and the line through \( D \) parallel to \( EF \) meets \(AC , AB\) at \( Q,R\) respectively. Let \( N\) be a point on the side \(BC\) such that \(\angle NQP +\angle NRP = 178^\circ\).
Which of the following is true?