如图,已知:AB平行CD,AC BD交与点O,OE平行AB交BC于点E求证1/AB+1/DC=1/OE

如图,已知:AB平行CD,AC BD交与点O,OE平行AB交BC于点E
求证1/AB+1/DC=1/OE

∵OE∥AB ,∴OE/AB=CE/BC,
∵OE∥DC,∴OE／DC＝BE／BC
两者相加：OE／AB＋OE／DC＝CE／BC＋BE／BC
因为CE+BE=BC,所以OE／AB＋OE／DC＝1,两边分别乘以1/OE,既得1/AB+1/DC=1/OE