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847 B
847 B
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\because \angle BAC=100^{\circ},BD=1\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！ -
做
\triangle ABD的外接圆,设交BC于E点 -
性质：圆的内接四边形对角互补
\therefore \angle BED=180^{\circ}-100^{\circ}=80^{\circ}\therefore \angle BDE=180^{\circ}-20^{\circ}-80^{\circ}=80^{\circ}\therefore BD=BE=1双
\because \angle BED=\angle BCD+\angle CDE \Rightarrow 80^{\circ}=40^{\circ}+\angle EDC\therefore \angle EDC=40^{\circ}\therefore ED=EC=\sqrt{3}-1 -
性质：圆周角相等对应的弦相等
\therefore AD=DE\therefore AD=\sqrt{3}-1