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第二十八章　圆
28.4 垂径定理*
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．已知在圆内接四边形ABCD中，∠A∶∠B∶∠C＝9∶8∶3，则∠D的度数为(　　)
A．15° B．120° C．30° D．60°
2．如图，AB为⊙O的直径，D为⊙O上一点，若∠CAB＝36°，则∠ADC的大小是________．
INCLUDEPICTURE"册124.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册124.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册124.tif" \* MERGEFORMATINET (第2题)　　　　　INCLUDEPICTURE"册125.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册125.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册125.tif" \* MERGEFORMATINET (第3题)
3．[2023安庆期中]如图，在△ABC中，∠C＝90°，AC＝9，AB的垂直平分线EF交AC于点D，交AB于点E，连接BD，若BD＝5，则DE的长是________．
INCLUDEPICTURE"预习效果检测.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果检测.tif" \* MERGEFORMATINET
1．垂直于弦的直径________这条弦，并且________这条弦所对的两条弧．
2．[2023嘉兴期中]如图，在⊙O中，AB是直径，CD是弦，AB⊥CD，垂足为E，连接CO，AD，∠BAD＝20°，则下列选项中错误的是(　　)
A．∠BOC＝2∠BAD B．BE＝EO
C．∠OCE＝50° D．CE＝DE
INCLUDEPICTURE"册126.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册126.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册126.tif" \* MERGEFORMATINET (第2题)　　　　　INCLUDEPICTURE"册127.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册127.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册127.tif" \* MERGEFORMATINET (第3题)
3．[2023福州期中]绍兴市是著名的桥乡，如图，石拱桥的拱顶到水面的距离CD为8 m，桥拱半径OC＝5 m，则水面宽AB为________m.
4．如图，AB是⊙O的直径，弦CD⊥AB于点E，若OE＝3，CD＝8.求⊙O的半径．
INCLUDEPICTURE"册128.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册128.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册128.tif" \* MERGEFORMATINET
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
INCLUDEPICTURE"W21.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\W21.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\W21.tif" \* MERGEFORMATINET
知识点1 垂径定理
INCLUDEPICTURE"L1.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L1.tif" \* MERGEFORMATINET 如图，⊙O的半径为5，弦AB＝8，OC⊥AB，垂足为点P，则CP的长等于(　　)
INCLUDEPICTURE"册129.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册129.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册129.tif" \* MERGEFORMATINET
A．2 B．2.5 C．3 D．4
变式1－1如图，AB是⊙O的弦，OD⊥AB于点D，延长OD交⊙O于点E，C为上一点，则下列说法错误的是(　　)
INCLUDEPICTURE"册130.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册130.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册130.tif" \* MERGEFORMATINET
A．AD＝BD B．∠ACB＝∠AOE
C.＝ D．OD＝DE
变式1－2如图，AB为⊙O的直径，AE为⊙O的弦，C为优弧ABE的中点，CD⊥AB，垂足为D.若AE＝8，DB＝2，则⊙O的半径为(　　)
INCLUDEPICTURE"册131.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册131.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册131.tif" \* MERGEFORMATINET
A．6 B．5 C．4 D．4
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知识点2 垂径定理的应用
INCLUDEPICTURE"L2.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L2.tif" \* MERGEFORMATINET 一条排水管的截面如图所示，已知排水管的半径OB＝5，水面宽AB＝8，则截面圆心O到水面的距离OC是(　　)
INCLUDEPICTURE"册132.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册132.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册132.tif" \* MERGEFORMATINET
A．3 　　 B．4 　　 C．3 　　 D．6
变式2[2023武汉期中]如图是一个高速公路的隧道的横截面，它的形状是以O为圆心的圆的一部分，如果D是⊙O中弦AB的中点，CD经过圆心O交⊙O于点C，AB＝24，CD＝18，则此圆的半径OA的长为________．
INCLUDEPICTURE"册133.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册133.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册133.tif" \* MERGEFORMATINET
28.4 垂径定理*
INCLUDEPICTURE"复习回顾.tif" INCLUDEPICTURE "复习回顾.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\复习回顾.tif" \* MERGEFORMATINET
1．D　2.54°　3.
INCLUDEPICTURE"预习效果.tif" INCLUDEPICTURE "预习效果.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\预习效果.tif" \* MERGEFORMATINET
1．平分； 平分　2.B　3.8
4．解：连接OC，
∵AB是⊙O的直径，AB⊥CD，
∴CE＝CD＝4.
在Rt△COE中，由勾股定理，得OC＝＝＝5.∴⊙O的半径为5.
INCLUDEPICTURE"课堂导学.tif" INCLUDEPICTURE "课堂导学.tif" \* MERGEFORMAT INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\课堂导学.tif" \* MERGEFORMATINET
例1　A　变式1－1.D　变式1－2.B　
例2　A　变式2.13

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