1、高中數學 122圓的切線的判定和性質課件 北師大版選修41ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航1.復習、回顧直線與圓的位置關系及其判斷方法.2.理解并掌握切線的判定定理、性質定理及推論.3.理解切線長定理.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SU

2、ITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI T

3、OUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導

4、航124356ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航124356【做一做4】 直線l與O相切,P是l上任一點,當OPl時,則().A.點P不在O上B.點P在O上C.點P不可能是切點D.OP大于O的半徑解析:由于OPl,則P是l與O的切點,則點P在O上.答案:BZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHUL

5、I知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456【做一做5】 直線l與O相切于點P,在經過點P的所有直線中,經過點O的直線有().A.1條B.2條C.3條D.無數條解析:過點P且垂直于l的直線僅有1條,此時圓心O在該垂線上,故選A.答案:AZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO

6、重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航123456ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航1.與圓的切線有關的知識剖析:(1)切線和圓只有一個公共點;(2)切線和圓心的距離等于圓的半徑;(3)切線垂直于過切點的半徑;(4)經過圓心且垂直于切線的直線必過切點;(5)經過切點且垂直于切線的直線必過圓心.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIA

7、N隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航2.判定切線的方法剖析:判定切線通常有三種方法:(1)定義法:和圓有唯一一個公共點的直線是圓的切線;(2)距離法:到圓心的距離等于半徑的直線是圓的切線;(3)定理法:過半徑外端且和該半徑垂直的直線是圓的切線.“過半徑外端,垂直于這條半徑的直線是圓的切線”是“到圓心的距離等于半徑的直線是圓的切線”的具體化.在使用時要根據題目的具體要求選取合適的方法.若已知要證的切線經過圓上一點,則需把這點與圓心相連,證明這條直線與此半徑垂直,即用定理法;若不能確定要證明的切線與圓有公共點,則需先向這條直線作垂線,再證明此垂線段是圓的半徑

8、,即用距離法證明.通常不用定義法證明.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航題型一題型二題型三ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航題型一題型二題型三ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航題型一題型

9、二題型三ZHISHI SHULIZHISHI SHULIZHISHI SHULIZHISHI SHULI知識梳理知識梳理知識梳理知識梳理ZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAO重難聚焦重難聚焦重難聚焦重難聚焦SUITANGYANLIANSUITANGYANLIANSUITANGYANLIANSUITANGYANLIAN隨堂演練隨堂演練隨堂演練隨堂演練DIANLI TOUXIDIANLI TOUXIDIANLI TOUXIDIANLI TOUXI典例透析典例透析典例透析典例透析MUBIAODAOHANGMUBIAOD

10、AOHANGMUBIAODAOHANGMUBIAODAOHANG目標導航目標導航目標導航目標導航題型一題型二題型三證明:(1)如圖所示,連接OC.PD切O于點C,OCPD.又BDPD,OCBD.1=3.又OC=OB,2=3.1=2.BC平分PBD.(2)如圖所示,連接AC.AB是O的直徑,ACB=90.BDPD,ACB=CDB=90.又1=2,ABCCBD.BC2=ABBD.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航題型一題型二題型三ZHISHI SHULI知識梳理

11、ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航題型一題型二題型三證明:如圖所示,連接OE.OA=OE,OEA=OAE.又AE平分BAF,OAE=EAF.OEA=EAF.OEAD.ADCD,OECD.CD與O相切于點E.即CD是O的切線.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航題型一題型二題型三ZHISHI SHULIZHISHI SHULIZHISHI SHULIZHIS

12、HI SHULI知識梳理知識梳理知識梳理知識梳理ZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAO重難聚焦重難聚焦重難聚焦重難聚焦SUITANGYANLIANSUITANGYANLIANSUITANGYANLIANSUITANGYANLIAN隨堂演練隨堂演練隨堂演練隨堂演練DIANLI TOUXIDIANLI TOUXIDIANLI TOUXIDIANLI TOUXI典例透析典例透析典例透析典例透析MUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANG目標導航目標導航目標導航

13、目標導航題型一題型二題型三證明:如圖所示,連接OB,OC,OD,OD交BC于點E.DCB是所對的圓周角,BOD是所對的圓心角,BCD=45,BOD=90.ADB是BCD的一個外角,DBC=ADB-ACB=60-45=15.DOC=2DBC=30.BOC=BOD+DOC=120.OB=OC,OBC=OCB=30.在OEC中,EOC=ECO=30,OE=EC.在BOE中,BOE=90,EBO=30,BE=2OE=2EC.ABOD.ABO=90.故AB是BCD的外接圓的切線.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOU

14、XI典例透析MUBIAODAOHANG目標導航題型一題型二題型三ZHISHI SHULIZHISHI SHULIZHISHI SHULIZHISHI SHULI知識梳理知識梳理知識梳理知識梳理ZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAO重難聚焦重難聚焦重難聚焦重難聚焦SUITANGYANLIANSUITANGYANLIANSUITANGYANLIANSUITANGYANLIAN隨堂演練隨堂演練隨堂演練隨堂演練DIANLI TOUXIDIANLI TOUXIDIANLI TOUXIDIANLI TOUXI典例透析典例透析

15、典例透析典例透析MUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANG目標導航目標導航目標導航目標導航題型一題型二題型三證明:EA,EF,FB是O的切線,EA=EC,FC=FB.EA,FB切O于點A,B,AB是直徑,EAAB,FBAB.EAFB.CPFB.EPC=EBF.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航題型一題型二題型三ZHISHI SHULIZHISHI SHULIZHISHI SHULIZHISHI S

16、HULI知識梳理知識梳理知識梳理知識梳理ZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGNAN JVJIAO重難聚焦重難聚焦重難聚焦重難聚焦SUITANGYANLIANSUITANGYANLIANSUITANGYANLIANSUITANGYANLIAN隨堂演練隨堂演練隨堂演練隨堂演練DIANLI TOUXIDIANLI TOUXIDIANLI TOUXIDIANLI TOUXI典例透析典例透析典例透析典例透析MUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANG目標導航目標導航目標導航目標導航

17、題型一題型二題型三解:設RtABC的內切圓與三邊相切于點D,E,F.連接OD,OE,OF,則ODAC,OEBC,OFAB.O與RtABC的三邊都相切,AD=AF,BE=BF,CE=CD.設AD=x,BE=y,CE=r,則有解得r=.即RtABC的內切圓半徑為.ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航1 2 3 4 51已知AB是O的切線,在下列給出的條件中,能判定ABCD的是(). A.AB與O相切于直線CD上的點CB.CD經過圓心OC.CD是直線D.AB與O相切

18、于點C,CD過圓心OZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航1 2 3 4 5ZHISHI SHULI知識梳理ZHONGNAN JVJIAO重難聚焦SUITANGYANLIAN隨堂演練DIANLI TOUXI典例透析MUBIAODAOHANG目標導航1 2 3 4 5ZHISHI SHULIZHISHI SHULIZHISHI SHULIZHISHI SHULI知識梳理知識梳理知識梳理知識梳理ZHONGNAN JVJIAOZHONGNAN JVJIAOZHONGN

19、AN JVJIAOZHONGNAN JVJIAO重難聚焦重難聚焦重難聚焦重難聚焦SUITANGYANLIANSUITANGYANLIANSUITANGYANLIANSUITANGYANLIAN隨堂演練隨堂演練隨堂演練隨堂演練DIANLI TOUXIDIANLI TOUXIDIANLI TOUXIDIANLI TOUXI典例透析典例透析典例透析典例透析MUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANGMUBIAODAOHANG目標導航目標導航目標導航目標導航1 2 3 4 5解析:如圖所示,連接AB.AOC=120,AOB=60.又OA=OB,AOB是等邊三角形,OB=AB.又OB=BP,AB=OP,OAP=90.即OAAP,則PA與O相切.答案: