# A comparison of lengths

Level pending

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?

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