垂直弦的直径（垂径定理）
![](https://wkrtcs.bdimg.com/rtcs/image?w=119&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"119","h":"118","dataType":"png","c":"word/media/image1_1.png","imgOriW":1245,"imgOriH":1226})
一、复习与思考：
1．如下图，弦AB对应的弧为为 ；此图是不是轴对称图形？如果是，求你画出它的一条对称轴.
二、新课学习
垂径定理：垂直于弦的直径________弦，并且平分弦所对的两条________．
![](https://wkrtcs.bdimg.com/rtcs/image?w=102.8&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"102.8","h":"130.93333333333","dataType":"png","c":"word/media/image2.png","imgOriW":253,"imgOriH":323})
几何语言：∵________________，
∴________________；________________ ；________________.
垂径定理的推论
平分弦(不是直径)的直径________弦，并且________弦所对的弧．
∵________________，
∴________________；________________；________________.
练习：
2．如图，CD是⊙O的直径，CD⊥AB，则下列结论：①EA＝EB②EO＝ED③![](https://wkrtcs.bdimg.com/rtcs/image?w=65&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"65","h":"23","dataType":"gif","c":"word/media/image3.png"})
④.一定成立的有
3．如图，在⊙O中，半径OC⊥AB于点E，AE＝2，则下列结论正确的是（ ）
A．OE＝2 B．EC＝2 C．AB垂直平分OC D．OC垂直平分AB
![](https://wkrtcs.bdimg.com/rtcs/image?w=140&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"140","h":"128","dataType":"png","c":"word/media/image5_1.png","imgOriW":1457,"imgOriH":1332})
第2题 第3题 第4题 第5题
4．如图，在⊙O中，直径CD⊥弦AB，AB＝8，OE＝3，则⊙O半径为 及ED的长为 ．
5．如图，⊙O半径为5，OC＝3，OC⊥AB，求AC的长为 及AB的长为 ．
![](https://wkrtcs.bdimg.com/rtcs/image?w=110.66666666667&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"110.66666666667","h":"137.33333333333","dataType":"gif","c":"word/media/image8.png"})
6．如图，在⊙O中，直径CD⊥AB，AB＝6，ED＝1，求⊙O半径．
7．如图，是一个高速公路的隧道的横截面，若它的形状是以O为圆心的圆的一部分，路面AB=12米，拱高CD=9米，求圆的半径．
![](https://wkrtcs.bdimg.com/rtcs/image?w=110&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"110","h":"102","dataType":"png","c":"word/media/image9.png","imgOriW":110,"imgOriH":102})
小结：“垂径三角形五线段，知二求三”
![](https://wkrtcs.bdimg.com/rtcs/image?w=147&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"147","h":"163","dataType":"png","c":"word/media/image10_1.png","imgOriW":1226,"imgOriH":1364})
8．如图，AB是⊙O的弦，点C，D是直线AB上的点，且OC＝OD.求证AC＝BD.
![](https://wkrtcs.bdimg.com/rtcs/image?w=160&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"160","h":"100","dataType":"png","c":"word/media/image11.png","imgOriW":417,"imgOriH":260})
9．如图，在平面直角坐标系中，点O为坐标原点，点P在第一象限，⊙P与x轴交于O，A两点，点A的坐标为（6，0），⊙P的半径为![](https://wkrtcs.bdimg.com/rtcs/image?w=28&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"28","h":"18","dataType":"png","c":"word/media/image12.png","imgOriW":28,"imgOriH":18})
，则点P的坐标为 ．
![](https://wkrtcs.bdimg.com/rtcs/image?w=152&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"152","h":"101","dataType":"png","c":"word/media/image13.png","imgOriW":169,"imgOriH":112})
10．如图，AB为⊙O的直径，E为OB与CD的中点.试猜想：△OBD是什么特殊三角形？四边形OCBD是什么特殊四边形？并证明你的猜想.
![](https://wkrtcs.bdimg.com/rtcs/image?w=130&md5sum=60ed86562f14359f00594a34420a73a6&sign=eed1e969d6&rtcs_flag=1&rtcs_ver=3&l=webapp&bucketNum=109&ipr={"t":"img","w":"130","h":"128","dataType":"png","c":"word/media/image14_1.png","imgOriW":1351,"imgOriH":1332})
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