In the acute triangle ABC, ah is high, if AB + BH = HC, prove: angle B = 2, angle c (to process,) In the acute triangle ABC, ah is high, if AB + BH = HC, prove: angle B = 2, angle C

Thinking: cut short
Take point D on HC, BH = HD
∵AB+BH=HC,BH=HD
∴AB=AC
∵AH⊥BD,BH=HD
From ab = ad (three lines in one isosceles triangle), we can get ∠ B = ∠ ADH
Ad = CD deduces that ∠ C is equal to ∠ DAC
∠ ADH = 2 ∠ C = angle B

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