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圆周角

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圓周角C1與C2相等，C3與C4相等。同時C3的大小為圓心角α的一半。

在幾何學中，當圓的兩條割線在圓上相遇時，就會形成圓周角。

一般來說，圓周角可被視為共用一個端點的兩條弦。

历史

圓周角的基本性質記載於《幾何原本》第三卷的第20至22號命題。几何原本中的命题为：

  1. 圓周角大小為对同弧的圓心角一半
  2. 对同弧的圓周角相等
  3. 共用一弦的兩圓周角大小和為180°

定理

  • 圓周角大小為對同圆弧的圓心角的½
  • 同弧的圓周角相等或互补
    • 若两圆周角定点在弦所在直线的同一边，则两圆周角相等。
    • 若两圆周角定点分别在弦所在直线的两边，则圆周角互补。
    • 若两圆周角定点在一条直径上，则圆周角恒等于90°。[1]

参考资料

  1. ^ 人民教育出版社九年级上册数学书
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圆周角
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