Question

几何题急!如图,在△ABC中,有b^2=c^2-ac,求证∠ABD=2∠ACE.

Answer 1

因 b²=c²-ac

则

b:c=(c-a):b

令 BF＝a

则 AF＝c-a, △BCF为等腰△,∠BCF=∠BFC=∠ACF+∠CAF ----(1)

△ABC 相似於△ACF

∠ABC=∠ACF, ∠CAF=∠BAC ----(2)

而

∠ACE=∠BAC+∠ABC ---(3)

∠ABD=∠BAC+∠ACB

∠ACB=∠BFC+∠ACF=∠BAC+∠ACF+∠ACF

所以

∠ABD=2∠ACE