第三章圆知识归纳与题型突破(十三类题型清单)(原卷版)_初中全科知识点总结和试卷_赠送习题试卷_初中3年学习辅助资料_1、初中学习资料_4-2、数学

      
      
第三章 圆 知识归纳与题型突破（十三类题型清单） 
 !
1#
(1)&' OA )*+,-. O /0123,-. A 456789&2:;.
=         =(2)?@.ABCDE.FG.
H.
 IJKLM2NOKPQRK,STKJ2UKNO2VWXYZR
  =  [?\789&.
2#
(1)/0Y]
?/0^_`52)J/0a!bcdef`5gGR?hJ^
_`52^_hJ?J.
ijkCh2l,J!2l\m2l\n2l\nJA2opqrhasqtC2uv+4^
Swxyqz{tC.
==        (2)|^_
?|^_`52}~Ja&c?+^_|.
=        =(3)O‚ƒ
==       =IDnO„zo\n2…†„zn4^l\m.
01  思维导图
02  知识速记
      
      
==   =[„zn(Y?O)ODn2…†„zn4^l\m.
== =  ‡n„z&~J2†„zn^l\m.
==   =ˆ„z\n4^l\m&~J2†„z‰n.
==   =Š„‹nŒmtC.
H.
 i}w‚ƒh
~JDn„zn„zn4^m„zn4^Žm2i
o,\h2‘’asl,2“”‚•wx–,—ƒ.˜s
“~J„zn”›œž2„z
nY”?OŸ
3#l
==(1)l,?,|^_`52^_|?l J&.
==(2)t¡l J&„z¢n2t£l J&}~£..
4# !
==(1)J!
¥.iJ!:J!.
== =J!
J!b
CD+4^mb
.
==(2)1!
¥.i¦2l§cdt¡!:;1!.
== =1!
== =I1!CD+4^m4^J!N.
== =[jmkCm4^1!tCRijkCh2tC1!4^mtC.
== =‡90ª1!4^nœORNkO4^1!œ!.
== =ˆ«¬–!5§¦h&CDo§N2uvo,–!5?!–!5.
== =Š­®p§5^!¯°R±!CD+­^!.
H.
=(1)1!²³´µl,\
I¥.i¦R[!l§cdt¡.
=    =(2)1!6¶·¸\?ijkCh.
V LM¹
1#º,. P ?¼i½( ¦
==½O NOœ
2OP=
2¿ 
==
. P i½O ±R=
. P i½O ¦R
. P i½O ­.
H.
.dLM¹d.@JAB
r¹?t^S2À‘’LM¹“ZÁK
r¹R
‘’
r¹ÂZÁKLM¹.
2#ºÃ,.
1
2
n
A
A
A
L
、
、
ij,¦ÄÅ
==Æ
ž2
i½O ¦.
3#&dLM¹
==½O NOœ R2. O @& ABœ
.
==(1)& d½O È ¢.
&dtB
.
==(2)& d½O É¢.
& d½O t£
.
==(3)& d½O l,¢.
& d½O t¡
.
4#£&º
==(1)£&º
== =I}~NO±-…†Do\NO&?£&.
== =[@JAB
CDNO&?£&.
==(2)£&
== =I£&D~£.NO.
== =[}~J›£&&}~£..
== =‡}~£.›£&&}~J.
==(3)£&E
ʱ.›£&2o.d£.ËÌ&'Eb:;£&E.
==(4)£&E
ʱ.›l\£&2+Í£&EtC2o.dJ &„zl\£&
Œ!.
5#dLM¹
      
      
==
NOœ
2JA
.
==(1)
d
È ¢.2†Ï,¦4 .i3,±Ð
±B
== =
.
==(2)
d
È ¢.2†
Ï,.ci
­Ð
­Ñ
==(3)
d
 É¢.2Òo,.±2Ï,¦.ci3,±Ð
±£
.
==(4)
d
 É¢.2Òo,.±2
Ï,.ci
­Ð
­£
.
==(5)
d
 l,¢.
t¡
.
––!5±®­£­®p§5±£p§5
1#–!5­J±JgJJ
==(1)–!5­J
?–!5–\!„z&¡.2+?–!5­£J2i–!5­Ð2+@–
!5–§ABtC2ÓÔÕ“I”×Ø.
==(2)–!5±J
?–!5–§h&¡.2+?–!5±®J2Ù!–!5±Ji–!5
­Ð2!–!5±J?Ú§h.2Û!–!5±Ji–!5±Ð2–!5±J@–!5–,¥.A
BtC2ÓÔÕ O ×Ø.
==(3)–!5gJ
?–!5–§h&¡.2i–!5­ÐR+@¥.AB?@^§h.AB 2 Ü2
ÓÔÕ G ×Ø.
==(4)J
?–!5–§Þ&¡..
H.
=(1) aß,–!5c †à ,­£2áas,c â
,±£–!5R
==    (2) ãä–!5­J åž2æçÅ?ÔÕ2À–!5æçCD1E­£NOèç
N2À
(S œ–!5æç2P œ–!51E2r œ­£NO).
==   (3) –!5±J­Jë{
ì_
KÄÅ
`5

±J(–!5
±®
J)
–!5–§h&
¡.
(1)OA=OB=OCR(2)±JY
i–!5­Ð
­J(–!5
­£
J)
–!5–\!„z&
¡.
(1)@–!5–§ABtCR
(2)OAOBOC z{„zï
BACïABCïACBR (3)­
Ji–!5­Ð.
2#­®p§5d±£p§5
==(1)p,.ci¦p§5:­®p§52­®p§5^!¯°2±!CD­^!.
==(2)y§cdt£p§5:±£p§52±£p§5^§ËdtC.
ph ðñ
1#h ðñ
==æçò
21E
.
      
      
==J!œ
NOœ R mE
.
==J!œ
2NOœ R2mEœ ó5æç
.
==ô5æçH0œó5d–!5æçdõfðñ.
==ö÷æ`?,ø52ùæNOœ R2ú&Eœ öûçœ
2÷æçœ
2üæç
œ
.
==ý÷æþÿ`œó52ùæNOœ R2ú&Eœ 2ޜ
ý÷æçœ
2üæçœ
2ú&EýÞùæNOËÌ 
.
H.
==(1)^Dó5æçò2ĀHãJ!? 1ªó5æç?æç
2
À
R
==(2)ió5æçòh2ā–,r
ó5æç Só5NO Ró5J!2‘’whl,r“
ZÁÕă–,r.
==(3)ó5æçò
2ZĄąĆ\ćĈĉĊÕ2+–!5æçò
 .ċ
Č2ZċčĎďR
==(4)ó5l,æçòËÌĐ¹
.
đ=ĒēĔGĕĖ
ė
1#ĘęĚÅěK?˜      Ÿ
A#}~–.ZÁ›,
B#OY?n
C#Cm4^J!tC
D#tCJ!4^mtC
ĜĝĞğ
2#Ġ‘⊙O Oœ 52ġ PO=52¿. P ⊙O LM¹?˜    Ÿ
A#. P i⊙O ­ B#. P i⊙O ¦
C#. P i⊙O ±
D#âźĢ
3#ĘęģĤh
˜1ŸtCJ!4^mtCR˜2ŸCm4^ntCR˜3ŸEbtCl\m?CmR
˜4Ÿ?|^_`52aß\Oc?^_|#ěK ˜==Ÿ
A#0 ,
B#1 ,
C#2 ,
D#3 ,
4#ĘęĚÅYěK?˜    Ÿ
A#DnO„zo\n
B#n4^l\mh. &„zn
03  题型归纳
      
      
C#ijkCh2tC1!4^mtC
D#„znOn2…†„zn4^m
đV=O‚ƒ
ė
5#«`2𝐴𝐵?
O
e
n2NOOC
AB
^
2µœ D2
O
e
NOœ 52
1
CD = 2¿𝐴𝐵Eœ˜    Ÿ
A#4
B#6
C#8
D#10
ĜĝĞğ
6#«`2OA
OB
OC
2
2
c?
O
e
NO2 AC
OB
2
¡D. D#ġ
8
6
AD
CD
OD
=
=
=
，
2¿ BD Eœ               
  
7#ĥĦ?ħĨĩĪīĬĭĮįİıIJij2ĴĵĶħĨĩĪķĸĹĺĻļ2«`2. P ×ØĥĦ
,ĽĮľ2«` 2#ÆĥĦIJ›ž2ĽĮľĿ‹ŀO?Á|J O œJ2†JiĮæ¦Ä2ġŁĮ
æłŃn AB Eœ8m 2ĥĦIJ›ž2ĽĮľiĮæÁĘńPŅbœ 2m#¿NOœ        
#
8#⊙O NO? 102n AB
CD
∥
2
16
12
AB
CD
=
=
2
2¿n AB CD AB?˜    Ÿ
A#2
B#14
C#2 k 14
D#7 k 1
đ– J!
ė
9#«`2 AB ?
O
e
O2 


BC
CD
DE
=
=
2
48
COD
Ð
=
°2¿ÐBOE b
œ          
#
      
      
  
ĜĝĞğ
10#«`2i
O
e
h2
2
AB
CD
=
2uv˜   Ÿ
A# 

2
AB
CD
>
B# 

2
AB
CD
<
C# 
2
AB
CD
=
D# 
AB  
2CD PQ¹âÅčņ
11#«`2p§5 ABCD ­®
O
e
2 AC „z
BAD
Ð
2¿ĘꗃěK?˜   Ÿ
 
A# AB
AD
=
B# BC
CD
=
C# 

AB
AD
=
D#
BCA
DCA
Ð
= Ð
12#«`2i
O
e
h2 

AC
BC
=
2DE z{?NOOAOB h.2 ®OC
AC
2
2BC
CD
CE
2
2
2¿Ę
ꗃY6¶?˜    Ÿ
A# AC
BC
=
B#CD
CE
=
C#
AOC
COB
Ð
= Ð
D#CD
OA
^
      
      
đp ±®
ė
13#!–!5l§Ez{œ 6 d 82+±®NO?˜    Ÿ
A#2
B#4
C#5
D#Á¦cY^
ĜĝĞğ
14#i,!–!5h2l§Ez{? 52122uvo,–!5±®NO?     #
15#Ġ‘Rt
ABC
Ň
h2
90
6
8
A
AB
AC
Ð
=
°
=
=
，
，
2¿
ABC
V
±®NOœ˜==Ÿ
A#3
B#4
C#5
D#YK
16#ġ& l ¦ p. A2B2C2D2& l ± . P2¿}~`h–,.›2ńňZÁ›          
,#
đ 1!
ė
17#«`2 AB ?
O
e
O2C ?
O
e
¦.#ġ
66
BOC
Ð
=
° 2¿
A
Ð
= ˜    Ÿ
  
A#66°
B#33°
C# 24°
D#30°
ĜĝĞğ
18#«`2. A 2 B 2C ʼni
O
e
¦2ġ
50
AOB
Ð
=
° 2¿
ACB
Ð
b
?˜    Ÿ
A# 25°
B#50°
C#75°
D#100°
19#«`2
O
e
?
ABC
V
±®2ġ
30
ABO
Ð
=
° 2¿
ACB
Ð
b
?˜     Ÿ
      
      
  
A#50°
B#60°
C#65°
D#70°
20#«`2 AB CD ?
O
e
n2† AB
CD
=
2ġ
84
BOD
Ð
=
° 2¿
ACO
Ð
b
œ˜==Ÿ
A#42°
B# 44°
C# 46°
D# 48°
21#«`2△ABC ?⊙O ­®–!52AD⊥PC D D .2† ACŊ132CDŊ52ABŊ12 2 2¿⊙O 
OCD˜==Ÿ
A#13
2
2
B#15 2
C#13 2
D#17
đŋ ­®p§5
ė
22#«`2p§5 ABCD ­®D
O
e
2Ġ‘
140
ADC
Ð
=
° 2¿
ABC
Ð
PQ?˜    Ÿ
      
      
A#80°
B#100°
C#60°
D# 40°
ĜĝĞğ
23#iěÄ5Ōōh2Áō. O œJŎ2Ċŏ}~ō. A2B2…im¦Ő. C2D2 ®
AC
BC
AD
BD
2
2
2
2¿
ADB
Ð
b
œ˜Ÿ
A#135°
B#130°
C#120°
D#YK
24#i
O
e
h2 AB œO2. C œ¦.2őŽm AC Œn AC œŔ2¡ AB D. D2 ®CD #«`2
ġ. D J O YgG2
26
BAC
Ð
=
° 2¿
ACD
Ð
b
œ        
#
25#«`2p§5 ABCD ­®D
O
e
2
45
BAD
Ð
=
°2
2
BC =
2
2
CD =
2¿
O
e
NOœ˜    Ÿ
  
A#
5
B# 10
C# 2 5
D# 2 10
đŕ ěň§5
ė
26#«¬,ěň§5hJ!œ 45°2uvo,ěň§5§
?      
#
ĜĝĞğ
27#«`2ěŋ§5 ABCDEF ­®D
O
e
2. M i 
AB ¦2¿
CME
Ð
b
œ       
#
      
      
28#«`2 AE
DF
2
?ěŖ§5 ABCDEFGH l\^!&2¿ AE
DF =    #
29#«`2 O
e
?쏧5 ABCDE ­£2z{£
,
AB CD D. M2N2P ?m MPN ¦.2¿
MPN
Ð
b
œ      
°#
đŖ mEó5æç
ė
30#Ġ‘p§5 ABCD ?ø52
2
AB =
2
2 2
BC =
2Á. B œJ BC œNO¡ AD D. E2¿`hŗ
ŘÐzæçœ          
#
ĜĝĞğ
31#«`2N O h2O ABŊ302n CD∥AB2 
CD Eœ 6π2¿ř 
CD  AC2AD Ś6ŗŘÐzæç
œ       
#
      
      
32#«`2i„æ­őRt
ABC
Ň
)*!¥. C śžŜ/0 90°2Ń@ Rt
EFC
Ň
2ġ
5
AB =
2
1
CF = 2
¿ŗŘÐzæçœ          
#
33#«`2iRt
ABC
Ň
h2
90 ,
ACB
O
Ð
=
° e
?
ABC
V
­£2ġ
3,
4
AC
BC
=
=
2¿`hŗŘÐzæ
çœ            
#
34#«`2Ġ‘ěŋ§5 ABCDEF §Eœ 22Á. E œJ2EF EœNO›2¿ŏŁěŋ§5łŃ
 
DF Eœ        
#
35#«`2NOœ 6 ó5 AOB h2
90
AOB
Ð
=
° 2C ? 
AB ¦.2CD
OA
^
2CE
OB
^
2µz{œ
D2E2ġCD
CE
=
2¿`hŗŘÐzæçœ                    
#
36#«`2 AB ?
O
e
O2. C ?
O
e
¦.2. D i BA ŝE&¦2CD 
O
e
¡D3. E2
2
20
DE
OB
D
=
=
Ð
=
°
，
2¿ 
BC Ebœ        
˜—¬Şş πŸ#
      
      
  
đŠ &LM¹
ė
37#Ġ‘
O
e
NO r œ3cm 2J O @& l AB d œ4cm 2& l 
O
e
¢.,
œ˜==Ÿ
A#0 ,
B#1 ,
C#2 ,
D#Á¦cY^
ĜĝĞğ
38#
ABC
V
h2
6
AB
AC
=
=
2
4
BC =
2Á. A œJ25 œNOŎ2uvŏ BC LM¹?˜    Ÿ
A#tB
B#t£
C#t¡
D#Y”K
đš £&º
ė
39#«`2 AB ?⊙O O2 BC ¡⊙O D. D 2 DE
AC
^
D. E 2ĘęĚÅYěK?˜    Ÿ
A#ġ DE
DO
=
2¿ DE ?⊙O £&
B#ġ AB
AC
=
2¿ DE ?⊙O £&
C#ġCD
DB
=
2¿ DE ?⊙O £&
D#ġ DE ?⊙O £&2¿ AB
AC
=
ĜĝĞğ
40#«`2
ABC
V
§ BC 
O
e
t£D. B 2. A i
O
e
¦2 AC }~JO 2†
40
C
Ð
=
°2P œŽm AB
¦ĸ.2 ® AP 2 BP 2¿
P
Ð
b
œ˜    Ÿ
A#115°
B#125°
C#130°
D#140°
      
      
41#«`2iRt
ABC
Ň
h2
90
C
Ð
=
° 2 D ? AB ¦.2Á AD œO
O
e
 BC t£D. E 2 ®
AE  DE 2ġ
30
B
Ð
=
° 2
3
AC =
2¿ BD Eb?˜    Ÿ
A#
3
B# 2
C#3
D#2 3
đš ­£
ė
42#«`2
O
e
?
ABC
V
­£2ġ
80
A
Ð
=
° 2¿
BOC
Ð
b
œ˜   Ÿ
A# 40°
B#150°
C#130°
D#100°
ĜĝĞğ
43#«`2
ABC
V
­£
O
e
 AB
BC
AC


t£D. DEF2Ġ‘
4
3
5
AB
AC
BC
=
=
=
2
2
22¿ DE
E?˜     Ÿ
A# 10
5
B# 2 10
5
C# 3 10
5
D# 4 10
5
44#«`2 ABC
V
­£
O
e
z{
,
,
AB BC AC t£D.
,
,
D E F 2†
3,
2,
4
AD
BE
CF
=
=
=
2¿
ABC
V

1Eœ˜    Ÿ
      
      
A#18
B#17
C#16
D#15
đšV ­J
ė
45#«`2. I ? ABC
V
­J2ġ
70
C
Ð
=
°2¿
AIB
Ð
=        
#
ĜĝĞğ
46#«`2
ABC
V
1E?18cm 2. O ?
ABC
V
­J2~. O › EF
AB
∥
2 AC
BC
、
z{¡D. E
F2Ġ‘
6cm
AB =
2¿
CEF
Ň
1Eœ            
cm #
47#«`2i
ABC
V
h2 AB
AC
=
2. D i AC §¦2~
ABD
△
­J I › IE
BD
^
D. E #ġ
14
BD =
2
6
CD = 2¿ BE Eœ˜    Ÿ
  
A#8
B#9
C#10
D#11
48#«`2i
ABCD
Y
h2
3
AB = 2
5
AD = 2ő
ABD
△
Œ BD œŔŃ@ A BD
¢
V
2ġ A D
¢
}~
CBD
Ň
­J I2
      
      
¿ DI Eœ        
#
𹖠ãŢ
ė
49#«`2𝐴𝐵?
O
e
O2. C2D i
O
e
¦2ġ 

AD
CD
=
2Ăţ
∥
OD
BC #
ĜĝĞğ
50#«`2i
O
e
h2DE z{œNOOAOB ¦.2 AD
BE
=
2C œm AB h.2 ®CD CE 
CO 2Ăţ
CD
CE
=
#
51#«`2i
O
e
h2n AB
CD
2
t¡D. M2† AB
CD
=
#
(1)Ăţ
 AD
BC
=
R
(2) ®OM
BD
2
2ġ BD ?
O
e
O2
2
8
AB
AD
=
= 2ĂOM E#
52#«`2
ABC
V
h2 AB
AC
=
2Á AB œO›
O
e
2¡ BC D. D 2¡ AC D. E #
      
      
(1)Ăţ
 

BD
DE
=
R
(2)ġ
50
BAC
Ð
=
°2Ă
AOE
Ð
b
#
53#«`2 ABC
V
­®D
O
e
2C œ 
ACB h.2D i 
BC ¦2 ® AD #ġ AD
BC
^
2µœ E 2&OC
z{¡ AD 2 AB D. F 2G
(1)Ăţ
CG
AB
^
R
(2)Ăţ
 EF
DE
=
#
54#«`2iěÄ5Ōō`hŤ¶„æ!ťŦ¹2\m}~Ōō. 

0,4
A
 

4,4
B -
 

6,2
C -
2ŧ
iŌō`hŨ‹«Ęũ›
(1)įÕŌō&Ū•ŏm4iJ D .2i`¦Ŧ• D .R
(2) ® AD
CD

2¿
D
e
NOEœ__________#˜—¬ŞşĄ	Ÿ
(3)«¬. E ťŦœ

2, 2
-
2¿ E .i
D
e
__________#(ū“­”“±”k“¦”)
55#Ġ‘2i Rt ABC
V
h2
90
BAC
Ð
=
°2Á𝐴𝐵œO
O
e
 BC t¡D. E2i AC ¦Ő. D2ĊŃ
DE
AD
=
#
      
      
(1)Ăţ
𝐷𝐸?
O
e
£&R
(2)Æ
5
BC =
2
2
AD =
ž2Ă
O
e
NO#
56#«`2O œ Rt
ABC
Ň
±®2
90
ACB
Ð
=
°2
4 3
BC=
2
4
AC =
2. D ?O ¦ĸ.2†.C 
D z{LD AB l÷#
(1)ĂO NOR
(2)Æ
4 2
CD =
ž2Ă
ACD
Ð
b
R
(3) AD h.œ M 2i. D Ŀĸ~Ŭh2&'CM ńPŭœ_______#
57#«` 12 AB ?
O
e
O2. C ?O AB ¦Ä
O
e
¦.2
ACB
Ð
!„z&¡
O
e
D. D#
    
(1)ġ
10
AB =
2Ă BD E#
(2)«` 22~. C ›
O
e
£&¡ DA ŝE&D. G2Æ
30
ABC
Ð
=
°ž2Ăţ
 AC
CG
=
#
(3)«` 32i
O
e
­Ő. Q2ĊŃ AC
CQ
=
2 BQ
BD
=
2Æ
CQB
Ň
œ!–!5ž2Ă
CDB
Ð
b
#
58#Ġ‘
«`2
O
e
­l\n AB CD 2† AB
CD
^
D E 2OAœ
O
e
NO2 ® AC  BD #
      
      
(1)Ăţ
OAC
BCD
Ð
= Ð
R
(2)› EN
BD
^
D N 2ŝE NE ¡ AC D. H #Ăţ
 AH
CH
=
R
(3)i˜2Ÿ\Ę2›
60
EHF
Ð
=
° ¡ AB D. F 2. P i FE ¦2 ® PC ¡ HN D. L 2Æ
2 7
EL
HF
=
=
2
8
CL = 2
2
BE
PF
=
ž2Ă
O
e
NO#