题目内容
如图,⊙O1和⊙O2都经过A,B两点,经过点A的直线CD交⊙O1于C,交⊙O2于D,经过点B的直线EF交⊙O1于E,交⊙O2于F.求证:CE∥DF.
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证明:连接AB.
∵四边形ABEC是⊙O1的内接四边形,
∴∠BAD=∠E.
又∵四边形ABFD是⊙O2的内接四边形,
∴∠BAD+∠F=180°.
∴∠E+∠F=180°.
∴CE∥DF.
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∵四边形ABEC是⊙O1的内接四边形,
∴∠BAD=∠E.
又∵四边形ABFD是⊙O2的内接四边形,
∴∠BAD+∠F=180°.
∴∠E+∠F=180°.
∴CE∥DF.
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