As shown in the figure, △ ABC, ad is the midline, AE is the bisector of angles, CF ⊥ AE is f, ab = 5, AC = 2, find the length of DF

As shown in the figure, extending CF intersection AB at h, ∵ AE is the angular bisector, CF ⊥ AE, ≁ CF = FH, ah = AC, ∵ BH = ab-ah = AB-AC = 5-2 = 3, and ∵ ad is the midline, ≁ DF is the median line of △ BCH, ≁ DF = 12bh = 12 × 3 = 1.5

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