如图.点A、B、C、D在⊙O上,AC⊥BD于点E,过点O作OF⊥BC于F,求证: (1)△AEB∽△OFC; (2)AD=2FO.
问题描述:
如图.点A、B、C、D在⊙O上,AC⊥BD于点E,过点O作OF⊥BC于F,求证:
(1)△AEB∽△OFC;
(2)AD=2FO.
答
证明:(1)如图,连接OB,则∠BAE=12∠BOC,∵OF⊥BC,∴∠COF=12∠BOC,∴∠BAE=∠COF,又∵AC⊥BD,OF⊥BC,∴∠OFC=∠AEB=90°,∴△AEB∽△OFC;(2)∵△AEB∽△OFC,∴AEBE=FOFC,由圆周角定理,∠D=∠BCE,...