如图2-5-18,已知⊙O1与⊙O2相交于E、F两点,过E任作直线分别交⊙O1与⊙O

如图2-5-18,已知⊙O₁与⊙O₂相交于E、F两点,过E任作直线分别交⊙O₁与⊙O₂于A、B两点,G为AB的中点,直线FG分别交两圆于C、D.

求证:CG=DG.

图2-5-18

答案

证明

:由相交弦定理得AG·GE=CG·GF.

由割线定理得BG·GE=GD·GF.

∵AG=BG,∴AG·GE=BG·GE.

∴CG·GF=GD·GF.∴CG=DG.

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如图2-5-18,已知⊙O1与⊙O2相交于E、F两点,过E任作直线分别交⊙O1与⊙O

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