弦切角定理
证明
已知:線段与相切,弦切角所夹的弧是,是所对的圆周角。
求证:
证明:
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(1)当圆心在的上时,如图1.
- ∵与圆相切於点.
- ∴
- ∵是的直径.
- ∴
- ∴
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(2)当圆心在的外部时,如图2,作的直径,连结.
- ∵
- ∴,
- ∴
- 又∵
- ∴
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(3)当圆心在的内部时,如图3,作的直径,再连结.
- ∵,
- ,
- 又由(2)可知,,
- ∴
- 综上所述,可知.
参考文献
- 人民教育出版社中学数学室. 第1版. 北京: 人民教育出版社. 1996.12: 134–136. ISBN 7-107-12025-5.
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