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23 lines
847 B
23 lines
847 B
2 years ago
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- $\because \angle BAC=100^{\circ},BD=1$
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$\therefore$这是一个定线定角问题，可以使用辅助圆试试，辅助圆一般是这个角和这条边组成三角形的外接圆！
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- 做$\triangle ABD$的外接圆,设交$BC$于$E$点
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- 性质：圆的内接四边形对角互补
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$\therefore \angle BED=180^{\circ}-100^{\circ}=80^{\circ}$
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$\therefore \angle BDE=180^{\circ}-20^{\circ}-80^{\circ}=80^{\circ}$
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$\therefore BD=BE=1$
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双$\because \angle BED=\angle BCD+\angle CDE \Rightarrow 80^{\circ}=40^{\circ}+\angle EDC$
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$\therefore \angle EDC=40^{\circ}$
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$\therefore ED=EC=\sqrt{3}-1$
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- 性质：圆周角相等对应的弦相等
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$\therefore AD=DE$
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$\therefore AD=\sqrt{3}-1$
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