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第二十八章　圆
28. 3 圆心角和圆周角
第1课时　圆心角及其性质
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．找出图中所有的弦、优弧和劣弧．
INCLUDEPICTURE"册93.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册93.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册93.tif" \* MERGEFORMATINET
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．顶点在________的角叫做圆心角．
2．在同圆或等圆中，相等的圆心角所对的弦________，所对的弧__________．
3．在同圆或等圆中，两个圆心角及其所对应的两条弦和所对应的两条弧这三组量中，只要有一组量________，其他两组量就分别________．
4．在同圆或等圆中，若的长度等于的长度，则下列说法正确的有(　　)
①所对的圆心角等于所对的圆心角；②和是等弧；
③所对的弦长等于所对的弦长．
A．0个 B．1个 C．2个 D．3个
5．[2023丽水期中]如图，若∠AOB＝40°，则所对的圆心角的度数是________．
INCLUDEPICTURE"册94.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册94.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册94.tif" \* MERGEFORMATINET
6．如图，A，B，C，D是⊙O上的点，已知∠AOB＝∠COD，求证：AC＝BD.
INCLUDEPICTURE"册95.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册95.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册95.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 圆心角的概念
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 下面图形中的角是圆心角的是(　　)
　　　　　　　　　　　　
变式1下列说法正确的是(　　)
A．如果一个角的一边过圆心，则这个角就是圆心角
B．圆心角α的取值范围是0°＜α＜180°
C．圆心角就是顶点在圆心，且角的两边是两半径所在的射线的角
D．圆心角就是顶点在圆内的角
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知识点2 弧、 弦、圆心角之间的关系
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 [2023邢台期末]如图，AB是⊙O的直径，＝，∠COD＝50°，求∠AOD的度数．
INCLUDEPICTURE"册100.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册100.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册100.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　
变式2－1已知弦AB把圆周分成1∶3两部分，则劣弧AB所对圆心角的度数为(　　)
A．90° B．270° C．45° D．135°
变式2－2如图，A，B，C，D是⊙O上的点，如果AB＝CD，∠AOB＝70°，那么∠COD＝________．
INCLUDEPICTURE"册101.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册101.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册101.tif" \* MERGEFORMATINET
第2课时　圆周角及其性质
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．圆心角指顶点在________的角．
2．如图，AB，CD是⊙O的两条弦：
INCLUDEPICTURE"册102.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册102.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册102.tif" \* MERGEFORMATINET
①如果AB＝CD，那么____________，____________；
②如果＝，那么____________，____________；
③如果∠AOB＝∠COD，那么____________，____________．
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．顶点在________，两边都与圆________的角叫做圆周角．
2．圆周角定理：圆上一条弧所对的圆周角等于它所对的________的一半．
3．半圆(或直径)所对的圆周角是________，90°的圆周角所对的弦是________．
4．如图，所对的圆周角是__________，所对的圆周角是__________．
INCLUDEPICTURE"册103.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册103.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册103.tif" \* MERGEFORMATINET (第4题)　　INCLUDEPICTURE"册104.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册104.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册104.tif" \* MERGEFORMATINET (第5题)　　
5．[2023无锡期中]如图，A，B，C三点在⊙O上，且∠A＝50°，则∠BOC的度数为(　　)
A．100° B．120° C．130° D．150°
6．[2023杭州期中]如图，AB是⊙O的直径，点C在圆上，若所对的圆心角为64°，则∠CBA的度数为(　　)
(第6题)
A．32° B．64° C．68° D．58°
7．如图，点A，B，C在⊙O上，∠ACB＝50°，求∠OAB的度数．
INCLUDEPICTURE"小册1.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\小册1.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\小册1.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 圆周角
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 [2023唐山期末]下列图形中，∠BAC是圆周角的是(　　)
变式1如图，△ABC内接于⊙O，弦BD交AC于点P，连接AD.下列角中，是所对的圆周角的是(　　)
INCLUDEPICTURE"册110.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册110.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册110.tif" \* MERGEFORMATINET
A．∠APB B．∠ABD C．∠ACB D．∠BAC
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知识点2 圆周角定理
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 [2023邢台期末]如图，在⊙O中，∠AOB＝130°，则∠C的度数为________．
INCLUDEPICTURE"册111.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册111.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册111.tif" \* MERGEFORMATINET
变式2如图，在⊙O中，∠OBA＝34°，点D是上的一点，则∠ADB的度数为(　　)
INCLUDEPICTURE"册112.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册112.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册112.tif" \* MERGEFORMATINET
A．54° 　 B．56° C．58° D．60°
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　
知识点3 圆周角定理的推论
INCLUDEPICTURE"L3.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L3.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\L3.tif" \* MERGEFORMATINET 如图，在△ABC中，AB＝AC，∠C＝70°，以AB为直径的⊙O交BC于点D，则所对圆心角的度数为________°.
INCLUDEPICTURE"册113.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册113.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册113.tif" \* MERGEFORMATINET
变式3[2023周口期末]将一个含60°角的直角三角板和一个量角器按如图所示的方式放置，∠ACB＝90°，其中点D所在位置在量角器外侧的读数为30°，连接DC交AB于点E，则图中∠BEC的度数是(　　)
INCLUDEPICTURE"册114.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册114.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册114.tif" \* MERGEFORMATINET
A．75° 　 B．65° C．55° D．45°
第3课时　圆内接四边形及其性质
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．如图，点O是△ABC的外接圆的圆心，若∠A＝80°，则∠BOC的度数为(　　)
A．100° B．160° C．150° D．130°
INCLUDEPICTURE"册115.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册115.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册115.tif" \* MERGEFORMATINET (第1题)　　　INCLUDEPICTURE"册116.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册116.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册116.tif" \* MERGEFORMATINET (第2题)
2．如图，在四边形ABCD中，∠B与∠1互补，AD的延长线与DC所夹的∠2＝60°，则∠1＝________，∠B＝________．
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．________所对的圆周角相等．
2．四个顶点都在同一个圆上的四边形叫做____________，这个圆叫做四边形的________．
3．圆内接四边形的对角________．
4．[2023北京西城区期中]如图，A，B，C三点在已知的圆上，在△ABC中，∠ABC＝70°，∠ACB＝30°，D是上的一点，分别连接DB，DC，则∠D的度数为(　　)
A．30° B．80° C．90° D．70°
INCLUDEPICTURE"册117.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册117.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册117.tif" \* MERGEFORMATINET (第4题)　　　　　INCLUDEPICTURE"册118.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册118.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册118.tif" \* MERGEFORMATINET (第5题)
5．[2023北京西城区期中]如图，点A，B，C，D在⊙O上，∠DAB＝40°，则∠DCB的度数为(　　)
A．80° B．100° C．140° D．160°
6．在圆内接四边形ABCD中，∠A，∠B，∠C的度数的比是3∶2∶7，求四边形各内角的度数．
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 同弧所对的圆周角相等
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，AB是⊙O的直径，∠BCD＝50°，则∠ABD的度数是(　　)
INCLUDEPICTURE"册119.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册119.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册119.tif" \* MERGEFORMATINET
A．50° B．40° C．30° D．25°
变式1[2023许昌期末]如图，在⊙O中，弦AB，CD相交于点P，若∠A＝50°，∠APD＝82°，则∠B的大小是(　　)
INCLUDEPICTURE"册120.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册120.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册120.tif" \* MERGEFORMATINET
A．32° B．42° C．48° D．52°
　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　知识点2　圆内接四边形
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 [2023南京期中]如图，在△ABC中，AB＝AC，过点A，C的⊙O与BC，AB分别交于点D，E，连接DE.
(1)求证：DB＝DE；
(2)延长ED，AC相交于点P，若∠P＝33°，则∠A的度数为________°.
INCLUDEPICTURE"册121.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册121.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册121.tif" \* MERGEFORMATINET
　　　　　　　　　　　　　　　　
变式2－1[2023南昌期末]如图，点A，B，C都在⊙O上，∠C＝100°，则∠O＝(　　)
INCLUDEPICTURE"册122.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册122.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册122.tif" \* MERGEFORMATINET
A．110° B．120° C．150° D．160°
变式2－2已知在四边形ABCD中，∠B＝90°，AB＝3，BC＝4，CD＝，AD＝2，试判断A，B，C，D四点是否在同一个圆上，并说明理由．
INCLUDEPICTURE"册123.tif" INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册123.tif" \* MERGEFORMATINET INCLUDEPICTURE "D:\\课件\\九数JJ河北（北京）\\册123.tif" \* MERGEFORMATINET
28. 3 圆心角和圆周角
第1课时　圆心角及其性质
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．解：弦：弦AB，弦CD，弦AD；
优弧：，，，；
劣弧：，，，.
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．圆心　2.相等；也相等　3.相等；相等　4.D　5.40°
6．证明：∵∠AOB＝∠COD，
∴∠AOB＋∠BOC＝∠COD＋∠BOC，
即∠AOC＝∠BOD，∴AC＝BD.
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　D　变式1.C
例2　解：∵在⊙O中，AB是⊙O的直径，∴∠AOB＝180°.
∵＝，∴∠BOC＝∠COD＝50°，
∴∠AOD＝180°－50°－50°＝80°.
变式2－1.A　变式2－2.70°
第二十八章　圆
28. 3 圆心角和圆周角
第2课时　圆周角及其性质
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．圆心
2．①＝；∠AOB＝∠COD
②AB＝CD；∠AOB＝∠COD
③AB＝CD；＝
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．圆上；相交　2.圆心角　3.直角；直径
4．∠BDC；∠CBD，∠CAD　5.A　6.D
7．解：连接OB，∵∠ACB＝50°，
∴∠AOB＝2∠ACB＝100°.
∵OA，OB都是⊙O的半径，∴OA＝OB.
∴∠OAB＝∠OBA＝＝40°.
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　B　变式1.C　例2　65°　变式2.B
例3　40　变式3.D
第3课时　圆内接四边形及其性质
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．B　2.120°；60°
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．同弧　2.圆内接四边形；外接圆　3.互补　4.B　5.C
6．解：∵∠A，∠B，∠C的度数的比是3∶2∶7，
∴设∠A，∠B，∠C的度数分别为3x，2x，7x.
∵四边形ABCD是圆内接四边形，
∴∠A＋∠C＝180°，∠B＋∠D＝180°，
∴3x＋7x＝180°，∴x＝18°，
∴∠A＝3x＝54°，∠B＝2x＝36°，∠C＝7x＝126°.
又∵∠B＋∠D＝180°，
∴∠D＝180°－∠B＝180°－36°＝144°.
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　B　变式1.A
例2　(1)证明：∵AB＝AC，∴∠B＝∠C.
∵四边形AEDC为⊙O的内接四边形，
∴∠AED＋∠C＝180°，
又∵∠AED＋∠BED＝180°，
∴∠BED＝∠C，
∴∠BED＝∠B，∴DB＝DE.
(2)38
变式2－1.D　
变式2－2.解：连接AC，
∵在△ABC中，∠B＝90°，AB＝3，BC＝4，
∴AC＝＝＝5.
∵在△ADC中，AD2＋DC2＝22＋()2＝52＝AC2，
∴∠D＝90°，∴∠B＋∠D＝180°.
又∵∠B＋∠BCD＋∠D＋∠BAD＝360°，
∴∠BCD＋∠BAD＝180°，
∴A，B，C，D四点在同一个圆上．

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