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垂径定理

垂径定理. The diameter which is perpendicular to a chord of the circle …. bisects the chord. and the arc. 已知：在⊙ O 中， CD 是直径， AB 是弦， CD⊥AB ，垂足为 E 。求证： AE ＝ BE 。. C. O. E. A. B. D. 证明： 连结 OA 、 OB ，则 OA ＝ OB 。. 因为垂直于弦 AB 的直径 CD 所在的直线既是等腰三角形 OAB 的对称轴又是⊙ O 的对称轴，.

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垂径定理

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  1. 垂径定理 The diameter which is perpendicular to a chord of the circle … bisectsthe chord and the arc.

  2. 已知：在⊙O中，CD是直径，AB是弦，CD⊥AB，垂足为E。求证：AE＝BE。已知：在⊙O中，CD是直径，AB是弦，CD⊥AB，垂足为E。求证：AE＝BE。 C . O E A B D 证明：连结OA、OB，则OA＝OB。 因为垂直于弦AB的直径CD所在的直线既是等腰三角形OAB的对称轴又是⊙ O的对称轴， 所以，当把圆沿着直径CD折叠时，CD两侧的两个半圆重合，A点和B点重合，AE和BE重合。 因此，AE＝BE。

  3. C . O E A B D 垂直于弦的直径平分这条弦 并且平分弦所对的两条弧。 题设 结论 平分弦 平分弦所对的优弧 平分弦所对的劣弧 过圆心 垂直于弦 ｝

  4. × 平分弦的直径垂直于弦。 平分弦（不是直径）的直径垂直于弦 ，并且平分弦所对的两条弧。 弦的垂直平分线经过圆心，并且平分弦所对的两条弧。 A perpendicular bisector of a chord passes through the centre and bisects the arc. A diameter bisecting a chord ( not diameter ) is perpendicular to the chord and bisects the arc. 平分弦所对的一条弧的直径，垂直平分弦，并且平分弦所对的另一条弧。

  5. 根据垂径定理及其推论可知对于一个圆和一条直线来说。如果具备根据垂径定理及其推论可知对于一个圆和一条直线来说。如果具备 （1）过圆心 （2）垂直于弦 （3）平分弦 （4）平分弦所对的优弧 （5）平分弦所对的劣弧 上述五个条件中的任何两个条件都可以推出其他三个结论。

  6. When you find the first mushroom ( 蘑菇 ) ， you should look aroud because they always grow together.

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