已知:如图,△ABC内接于圆,AD⊥BC于D,弦BH⊥AC于E,交AD于F.求证:FE=EH.
问题描述:
已知:如图,△ABC内接于圆,AD⊥BC于D,弦BH⊥AC于E,交AD于F.求证:FE=EH.
答
证明:连接AH,∵AD⊥BC,BH⊥AC,∴∠FDB=∠AEF=90°,∵∠AFE=∠BFD,∴∠EAF=∠FBD,∵∠HAC=∠HBC,∴∠HAE=∠EAF,∵BH⊥AC,∴∠AEF=∠AEH=90°,在△AEF和△AEH中,∠DAE=∠HAEAE=AE∠AEF=∠AEH∴△AEF≌...