九年级数学圆的知识点总结大全

1、amende d Decree No. 344 2011.12.1 the State Council promulgated by DecreeNo. 591, 9 People's Republic of Chi na regulations on r oad transport 2004.07.012004.01.13 10 safety production licenseOrdi nance, pr omulgatedby Decree No. 406 of the State Council promulgated by Decreeof the State Council

2、, No. 397 112007.06.01productionsafety acci dent re porting, investigation and handli ng of Ordinancepromulgated by De cree No. 493, 12 ofthe State Council regulations on special equipment safety supervision 2009.05.01 amendedDecre e No. 373 State Council DecreeNo. 549, 13 insura nce regulations reg

3、arding industrial injurie s 2011.01.01 amendment, promulgatedby Decre e No. 586 of the State Council promulgated by Decree No. 375, 14 administration of precursor chemicalsOrdi nance 2005.11.01 State Council DecreeNo. 445, 15 workplaces where toxic substances areuse d to labour protection 2002.05.12

4、 the State Council promulgated by Decree No. 352, 16 women workers . 4.6 review and revision 4.6.1production technology secti on Office organized relevantdepartme nts units once a year to review the documentation issued by, not suitablmaterial changes on or after an accident, and biotech branch and

5、that the workshopshoul d be timely to various reg ulations and safety rules be revised to ensure suitability and effectiveness. 4.6.3 revision of the file change approval form should be filled in, i ndi cating the causes andcha nges, a ppr oved by the Deputy incharge of security, General Manager of

6、revision. 4.6.4 anew revised safety regulations and safety rules shouldbe released to the post in a timely manner to ensure rules a ndsafety regulations of each post is the latest file, recover theoriginal documentunifie d void. 5. related records 5.1 list of applicable laws, regulations a nd standa

7、rdsof the inventory listingnumber carbon industry laws and regulations legal regulations and other requirementscame into for ce date enacte d se ctor update record 1/standardnumber Pe ople's Republicof China 2, Chairmanof the national people's Congress made the 70th producti on safety law 20

8、02.11.1 Peopl e's Republicof China La w of occupational diseaseprevention 2002.05.01labor law 2008.1.1, Chairmanof the nationalpeople's Congress Standing Committee, 65th 5People's Republic of China on road traffic safety law 2011.5.1, Chairmanof the national people's Congress made th

9、e 47th, 6People's Republic of China Trade Union law 2001.10.27 7,Chairman of the national people' s Congress made the 62nd People's Republic of China emergency response law 2007.11.1,Chairman of the nationa l pe ople's Co ngress, the 69t h 8 Hazardous chemical safety management regul

10、ation amende d Decree No. 344 2011.12.1 the State Council promulgated by DecreeNo. 591, 9People's Republi c of China regulations on road transport 2004.07.012004.01.13 10 safety production license Ordinance,第四章：圆一、知识回顾圆的周长 ： C=2 r 或 C=d、圆的面积 ：S=r 2圆环面积计算方法： S= R2- r 2或 S=（ R2-r 2）(R 是大圆半径， r 是小圆

11、半径）二、知识要点一、圆的概念集合形式的概念：231 、 圆可以看作是到定点的距离等于定长的点的集合；、圆的外部：可以看作是到定点的距离大于定长的点的集合；、圆的内部：可以看作是到定点的距离小于定长的点的集合轨迹形式的概念：1、圆：到定点的距离等于定长的点的轨迹就是以定点为圆心，定长为半径的圆；固定的端点 O为圆心。连接圆上任意两点的线段叫做弦，经过圆心的弦叫直径。 圆上任意两点之间的部分叫做圆弧，简称弧。2、垂直平分线：到线段两端距离相等的点的轨迹是这条线段的垂直平分线；3、角的平分线：到角两边距离相等的点的轨迹是这个角的平分线；4、到直线的距离相等的点的轨迹是：平行于这条直线且到这条直线的

12、距离等于定长的两条直线；5、到两条平行线距离相等的点的轨迹是：平行于这两条平行线且到两条直线距离都相等的一条直线。二、点与圆的位置关系1、点在圆内dr点C在圆内；Ad2、点在圆上dr点 B 在圆上；rOB3、点在圆外dr点 A 在圆外；dC三、直线与圆的位置关系1、直线与圆相离dr无交点；2、直线与圆相切dr有一个交点；3、直线与圆相交dr有两个交点；rd=rrdd四、圆与圆的位置关系promulgatedby De cree No. 406 of the State Councilpromulgatedby Decreeof the State Council,No. 397 11 2007

13、.06.01 production safety accident reporting, investigation a ndhandlingof Ordi na nce promulgated by De cree No.493,12 of the State Council regulations on special equipment safety supervision 2009.05.01 amende d Decree No. 373 State Council DecreeNo. 549, 13 insurance r egulations regarding i ndustr

14、ial injuries 2011.01.01 amendment,promulgated by Decree No. 586 of the State Councilpromulgated by DecreeNo. 375,14 admi nistration of precursor chemicals Ordinance2005.11.01 StateCouncil De cree No. 445, 15 workplace s where toxicsubstances areused to labour protection 2002.05.12 the State Councilp

15、romulgatedby De cree No. 352, 16 women workers . 4.6. review and revise 4.6.1production te chnol ogy section Officeonce every year and organize relev ant departments to review unit on the issuing of system files, not suitable documents be revised i n a timely manner.revisionof the filecha nge approv

16、al form shouldbe filled in, i ndi cating the cause s and changes, approved by the De puty in charge of security, General Manager of revision. 4.6.4 a new revised safety regulations and safety rulesshould be released to the post in atimely manner to ensure rules a nd safety regulationsof each post is

17、 the latest file, recover t he origi nal documentunified void. 5. related records5.1 list of applica ble laws, regulations and standards of the inventory listing number carbon industry laws and regulations legal regulations and other requirements came into forcedate ena cted se ctorupdate record 1 /

18、standardnumberPeople's Republicof Chi na 2,Chairman of thenationalpeople's Congress made the 70thproductionsafety law 2002.11.1 People's Republicof Chi naLaw of occupationaldisea se prevention 2002.05.01NPC3, or der of the Presi dentof the 60th People'Congre ss made the 47th, 6 Peopl

19、e's Republic of China Trade Union law 2001.10.27 7,Chairman of the national people'sCongress made the 62nd People's Republic of China emergency response law 2007.11.1, Chairmanof the nationalpeople'sCongress, the 69th8Hazardous chemical safety management regulation amended DecreeNo.

20、344 2011.12.1 the State Councilpromulgated by Decree No. 591, 9 People' s Republic of China regulationson road transport 2004.07.01 2004.01.13 10safety production license Ordinance, promulgated by Decree No. 406 of the State CouncilpromulgatedbyDecree of the State Council, No. 397 11 2007.06.01

21、production safety accident re porti ng, investigation and handling of Or dinance promulgated by Decree外离（图 1）无交点dRr ；外切（图 2）有一个交点dRr ；相交（图 3）有两个交点Rrd R r ；内切（图 4）有一个交点dRr ；内含（图 5）无交点dRr ；dddRrRrRr图 1图 2图 3ddrRrR图4图5五、垂径定理垂径定理：垂直于弦的直径平分弦且平分弦所对的弧。推论 1：（ 1）平分弦（不是直径）的直径垂直于弦，并且平分弦所对的两条弧；（2）弦的垂直平分线经过圆心，并且

22、平分弦所对的两条弧；（3）平分弦所对的一条弧的直径，垂直平分弦，并且平分弦所对的另一条弧以上共 4 个定理，简称 2 推 3 定理：此定理中共5 个结论中，只要知道其中2 个即可推出其它 3 个结论，即：AB是直径 ABCD CE DE 弧BC弧 BD 弧AC弧 AD中任意 2 个条件推出其他3 个结论。A推论 2：圆的两条平行弦所夹的弧相等。即：在 O 中， AB CDCDOO弧 AC弧 BDABEDCB六、圆心角定理顶点到圆心的角，叫圆心角。圆心角定理：同圆或等圆中，相等的圆心角所对的弦相等，所对的弧相等，弦心距相等。此定理也称 1 推 3 定理，即上述四个结论中，amende d Dec

23、ree No. 344 2011.12.1 the State Council promulgated by DecreeNo. 591, 9 People's Republic of Chi na regulations on r oad transport 2004.07.012004.01.13 10 safety production licenseOrdinance, promulgatedby Decree No. 406 of the State Council promulgated by Decreeof the State Council, No. 397 1120

24、07.06.01productionsafety acci dent re porting, investigation and handli ng of Ordinancepromulgated by De cree No. 493, 12 of the State Council regulations on special equipment safety supervision 2009.05.01 amendedDecre e No. 373 State Council DecreeNo. 549, 13 insura nce regulations regarding indust

25、rial injurie s 2011.01.01 amendment, promulgatedby Decree No. 586 of the State Council promulgated by Decree No. 375, 14 administration of precursor chemicalsOrdi nance 2005.11.01 State Council DecreeNo. 445, 15 workplaces where toxic substances areuse d to labour protection 2002.05.12 the State Cou

26、ncil promulgated by Decree No. 352, 16 women workers . 4.6 review and revision 4.6.1production technology secti on Office organized relevantdepartme nts units once a year to reviematerial changes on or after an accident, and biotech branch and that the workshopshoul d be timely to various reg ulatio

27、ns and safety rules be revised to ensure suitability and effectiveness. 4.6.3 revision of the file change approval form should be filled in, i ndi cating the causes andcha nges, a ppr oved by the Deputy incharge of security, General Manager of revision. 4.6.4 anew revised safety regulations and safe

28、ty rules shouldbe released to the post in a timely manner to ensure rules a ndsafety regulations of each post is the latest file, recover theoriginal documentunifie d void. 5. related records 5.1 list of applicable laws, regulations a nd standardsof the inventory listingnumber carbon indust ry laws

29、and regulations legal regulations and other requirementscame into for ce date enacte d se ctor update record 1/standardnumber Pe ople's Republicof China 2, Chairmanof the national people's Congress made the 70th producti on safety law 2002.11.1 Peopl e's Republicof China La w of occupati

30、onal diseaseprevention 2002.05.01labor law 2008.1.1, Chairmanof the nationalpeople's Congress Standing Committee, 65th 5People's Republic of China on road traffic safety law 2011.5.1, Chairmanof the national people's Congress made the 47th, 6People's Republic of China Trade Union law

31、 2001.10.27 7,Chairman of the nati onal people' s Congress made the 62nd People's Republic of China emergency response law 2007.11.1,Chairman of the nationa l pe ople's Congress, t he 69t h 8 Hazardous chemical safety management regulation amende d Decree No. 344 2011.12.1 the State Coun

32、cil promulgated by DecreeNo. 591, 9People's Republi c of China regulations on road transport 2004.07.012004.01.13 10 safety production license Ordinance,只要知道其中的1 个相等，则可以推出其它的E3 个结论，即： AOBDOE ；AB DE；FOOC OF ； 弧BA弧 BDDACB七、圆周角定理顶点在圆上，并且两边都与圆相交的角，叫圆周角。1、圆周角定理：同弧所对的圆周角等于它所对的圆心的即： AOB 和 ACB 是弧 AB 所对的

33、圆心角和圆周角 AOB 2 ACB2、圆周角定理的推论：推论 1：同弧或等弧所对的圆周角相等；同圆或等圆中，的弧是等弧；C角的一半。BOADC相等的圆周角所对即：在 O 中，C 、D 都是所对的圆周角CDBOA推论 2：半圆或直径所对的圆周角是直角；圆周角是直角所C对的弧是半圆，所对的弦是直径。即：在 O 中， AB 是直径或C90C90AB是直径BAO推论 3：若三角形一边上的中线等于这边的一半，那么这个三C角形是直角三角形。即：在 ABC 中， OC OA OBBOA ABC 是直角三角形或C90注：此推论实是初二年级几何中矩形的推论：在直角三角形中斜边上的中线等于斜边的一半的逆定理。八、

34、圆内接四边形圆的内接四边形定理：圆的内接四边形的对角互补，外角等于它的内对角。promulgatedby Decre e No. 406of the State Council promulgated by Decreeof the State Council, No. 39711 2007.06.01 production safety accident reporting, investigation and handling ofOrdina nce prom ulgated by DecreeNo. 493, 12of the State Council regulations on

35、special equipment safety supervision2009.05.01 amended Decree No. 373 State Council Decree No. 549, 13 insurance regulations regarding industrial injuries 2011.01.01 amendment, promulgated byDecreeNo. 586 of the State Council promulgated by Decree No. 375, 14 administration of precursor chemicalsOrd

36、inance 2005.11.01 State Council Decree No. 445, 15 workplaces where toxicsubstances are used to labour protection 2002.05.12 the State Councilpromulgated by De cree No. 352, 16 women workers . 4.6. review and revise 4.6.1production te chnol ogy sectionOff ice once every year and orga nize relevant d

37、epartments to review uniton the issuing of system files,not suitabledocuments be revised in a timely manner. 4.6.2 processes, technology, material changesonor after an accident, and biotech branch a nd that the workshop should be timely to various regulations a nd safety rules be revised to ensure s

38、uitability and effectiveness. 4.6.3revisionof the file change approval form shouldbe filled in, indicating the cause s and cha nges, a ppr oved by the De puty in charge of securit y, Ge neral Manager of revision. 4.6.4 anew revised safety regulations and safety rules should be released t o the p ost

39、 in a timely manner to ensure rules and safety regulationsof eachpost is the latest file, recover theoriginaldocumentunified v oid.5. related re cords 5.1 listof applicable laws, regulations and standards of the inventory listing num ber car bon industry laws a nd regulations legal regulations and o

40、ther requirements came into force date enacted sector update recor d 1/sta ndardnum ber Pe ople's Republic of China 2, Chairman of thenational peopl e's Congress made the 70th production safety law 2002.11.1 People' s Republicof Chi na Law of occupationa l disea se prevention 2002.05.01

41、NPC 3,order of thePresi dent of the 60th Peopl e's Republic of China fire control lawof 2009.05.01 4, Chairman of thenational people' s Congress Standi ng Committee 6thPeople's Republic of China labor law2008.1.1,Chairman of the national people'sCongress made the 47th, 6 People's

42、 Republic of China Trade Union law 2001.10.27 7,Chairma n of the nationalpeople's Congress made the 62nd People's Republic of China emergency response law 2007.11.1, Chairmanof the nati onalpeople'sCongress, the 69th 8Hazardous chemical safety management regulation amended Decree No. 344

43、 2011.12.1 the State Councilpromulgate d by Decree No. 591, 9 People's Republic of China regulationson road transport 2004.07.01 2004.01.13 10safety production license Or dinance, promulgated by Decree No. 406 of the State Councilpromulgatedby Decree of the State Council, No. 397 11 2007.06.01 p

44、roduction safety accident re porting, investigation and handling of Or dinance promulgated by Decree 3即：在 O 中，DC四边形 ABCD 是内接四边形CBAD180BD180DAECBAE九、切线的性质与判定定理（1）切线的判定定理：过半径外端且垂直于半径的直线是切线；两个条件：过半径外端且垂直半径，二者缺一不可即： MN OA 且 MN 过半径 OA外端MN 是O的切线O（2）性质定理：切线垂直于过切点的半径 （如上图）推论 1：过圆心垂直于切线的直线必过切MAN点。推论 2：过切点垂直于

45、切线的直线必过圆心。以上三个定理及推论也称二推一定理：即：过圆心；过切点；垂直切线，三个条件中知道其中两个条件就能推出最后一个。十、切线长定理切线长定理：从圆外一点引圆的两条切线， 它们的切线长相等，这点和圆心的连线平分两条切线的夹角。即： PA 、 PB 是的两条切线 PA PBPO 平分BPABOPA十一、圆幂定理（1）相交弦定理 ：圆内两弦相交，交点分得的两条线段的乘DBO积相等。P即：在 O 中，弦 AB 、 CD 相交于点 P ， PA PB PC PDCA（2）推论：如果弦与直径垂直相交， 那么弦的一半是它分直径段的比例中项。C所成的两条线BOEADamende d Decree

46、No. 344 2011.12.1 the State Council promulgated by DecreeNo. 591, 9 People's Republic of Chi na regulations on r oad transport 2004.07.012004.01.13 10 safety production licenseOrdinance, promulgatedby Decree No. 406 of the State Council promulgated by Decreeof the State Council, No. 397 112007.0

47、6.01productionsafety acci dent re porting, investigation and handli ng of Ordinancepromulgated by De cree No. 493, 12 of the State Council regulations on special equipment safety supervision 2009.05.01 amendedDecre e No. 373 State Council DecreeNo. 549, 13 insura nce regulations regarding industrial

48、 injurie s 2011.01.01 amendment, promulgatedby Decree No. 586 of the State Council promulgated by Decree No. 375, 14 administration of precursor chemicalsOrdi nance 2005.11.01 State Council DecreeNo. 445, 15 workplaces where toxic substances areuse d to labour protection 2002.05.12 the State Council

49、 promulgated by Decree No. 352, 16 women workers . 4.6 review and revision 4.6.1production technology secti on Office organized relevantdepartme nts units once a year to reviematerial changes on or after an accident, and biotech branch and that the workshopshoul d be timely to various reg ulations and safety rules be revised to ensure suitability and effectiveness. 4.6.3 revision of the file change approval form should be filled in, i ndi cating the causes andcha nges, a ppr oved by the Deputy incharge of security, General Manager of revision. 4.6.4 anew revised safety r