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问题 填空题

在△ABC中，AB=AC=5，若将△ABC沿直线BD翻折，使点C落在直线AC上的点C′处，AC′=3，则BC=______．

答案

如图，分两种情况：

①如图①，当C′在线段AC上时；

AC′=3，则CC′=2，C′D=CD=1；

在Rt△ABD中，AB=5，AD=AC′+C′D=4；

由勾股定理得：BD=3，

则BC=

BD2+CD2
=
10
；

②如图②，当C′在线段CA的延长线上时；

AC′=3，则CC′=8，C′D=CD=4；

在Rt△ABD中，AD=1，AB=5，

由勾股定理得：BD2=AB2-AD2=24，

则BC=

BD2+CD2
=2
10
；

故BC的长为

10
或2
10
．

选择题

下图所列内容为近代中国某历史事件的一些特征，据此推断该事件是

A．洋务运动

B．太平天国运动

C．义和团运动

D．戊戌变法
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I am honored to be here today, (1) Harvard at this celebration of the College Board’s half century of working to promote (2) and equal opportunity in higher education.
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