1 . 选修4-1:几何证明选讲
如图,在△ABC中,∠ABC=90°,以AB为直径的圆O交AC于点E,点D是BC边上的中点,连接OD交圆O与点M.
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573038525603840/1573038531895296/STEM/c12bc817a6ac47d788e5aa73e6b5e566.png)
(1)求证:DE是圆O的切线;
(2)求证:DE•BC=DM•AC+DM•AB.
如图,在△ABC中,∠ABC=90°,以AB为直径的圆O交AC于点E,点D是BC边上的中点,连接OD交圆O与点M.
![](https://img.xkw.com/dksih/QBM/2016/9/23/1573038525603840/1573038531895296/STEM/c12bc817a6ac47d788e5aa73e6b5e566.png)
(1)求证:DE是圆O的切线;
(2)求证:DE•BC=DM•AC+DM•AB.
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9-10高二下·新疆·阶段练习
2 . 已知:如图,在等腰梯形ABCD中,AD∥BC,AB=DC,过点D作AC的平行线DE,交BA的延长线于点E.求证:
![](https://img.xkw.com/dksih/QBM/2014/4/30/1571696661061632/1571696666591232/STEM/5017d5fc40b341f2be9a7d118199cc2d.png)
(1)△ABC≌△DCB;
(2)DE·DC=AE·BD.
![](https://img.xkw.com/dksih/QBM/2014/4/30/1571696661061632/1571696666591232/STEM/5017d5fc40b341f2be9a7d118199cc2d.png)
(1)△ABC≌△DCB;
(2)DE·DC=AE·BD.
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