Diagonal angles ∠FMP and ∠FNP of the quadrilateral FMPN are right angles, so this quadrilateral is an inscribed quadrilateral of a circle, and FP is the diameter of the circle. MN is a round string.

According to the theorem: the diameter perpendicular to the chord bisects the chord.

It can be concluded that MK=NK.

FP⊥MN in k, FK is a common edge.

So △FMK and △FNK are congruent

Introduction ∠MFK=∠NFK

So FP bisection ∠NFM is FP bisection ∠HFG.