数学证明题（圆）要过程

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0 | 2009-12-12 21:28:57 | 显示全部楼层 |阅读模式

联结OA，OB，OC，OD，过O作OG⊥DC交DC于G∵AC⊥BD于E∴∠AEB=Rt∠∴∠EAB+∠EBA=90°又∠AOD=2∠ABE，∠BOC=2∠EAB∴∠AOD+∠BOC=2(EAB+∠EBA)=180°又OA=OB=OC=OD，OF⊥AB，OG⊥CD∴2∠AOF=∠AOB，2∠DOG=∠DOC，DG=(1/2)DC∴∠AOF+∠DOG=90°又∠AOF+∠OAF=∠DOG+∠ODG=90°∴∠OAF=∠DOG，∠ODG=∠AOF又DO=AO∴△AOF≌△ODG∴OF=DG又DG=(1/2)DC∴OF=(1/2)CD