1、24.2.2 直线和圆的位置关系（三）核心目标.21课前预习.3课堂导学.45课后巩固.能力培优.核心目标 理解切线的性质定理，熟练运用圆的切线的性质解决问题课前预习1切线的判定定理：经过半径的_并且_于这半径的直线是圆的切线垂直外端2反过来，如右图，如果直线 是O的切线，切点为A，那么半径OA与直线l是不是一定垂直呢？试证明你的结论课前预习(1)完成下列证明过程：已知：如上图，直线 是O的切线，A为切点 求证：OAl 证明：假设OA与l不垂直，过 O作OMl，根据垂线段最短，OM_OA，即圆心到直线的距离_半径直线l与O_ 这与条件“直线l是O的切线”相矛盾，假设不成立，OAl.(2)通过上
2、述探究证明，可得到结论：圆的切_ _垂直于过切点的半径小于相交课堂导学知识点：切线的性质【例题】如右图，已知：RtABC中，点D在斜边AB上，以AD为直径的O与BC相切于点E，连接DE并延长，与AC的延长线交于点F.求证：ADAF.【解析】BC是O的切线，E为切点,连接OE，则OEBC,再结合ACBC,问题即可解决课堂导学【答案】证明：连接OE.BC是O的切线，OEBC.又ACBC，OEAC，OEDF.OEOD，OEDODE，FODE，ADAF.【点拔】在解有关圆的切线的问题时，常常需要作出过切点的半径课堂导学对点训练1如下图，PA为O的切线，A为切点，PO交O于点B，PA8，OA6，则PB_
3、2如上图，AB与O相切于点A，BO与O相交于点C，点D是 O上一点，B38.则D的 度数是_264课堂导学3已知ABC中，ABAC，DEAC于点E，DE与半O相切于点D.求证：ABC是等边三角形连接OD，则ODDE，又ACDE，ODAC，ODBA，OBOD，ODBOBD，OBDA，BCACAB，ABC是等边三角形课后巩固4如下图，AC是O的直径，PA切O于点A，弦BCOP，OP交O于点D，连接PB (1)求证：PB是O的切线；连接OB，BCOP，AOPOCB，BOPOBC，OCOB，OCBOBC，AOPBOP又OAOB，OPOP，AOPBOP，OBPOAP，PA与O相切，OAP90，OBP90
4、即OBPB，PB是O的切线课后巩固4如下图，AC是O的直径，PA切O于点A，弦BCOP，OP交O于点D，连接PB (2)若PA3，PD2，求O的半径设O的半径为rPA与O相切OAP90在RtAOP中，OA2AP2OP2即r232(r2)2解得r 54课后巩固5如下图，已知：ABC内接于O，B60，AD是O的切线，CO的延长线交AD于点D.(1)求D的度数；连接OA，则OAAD，又AOC2B120，AOD60，D30 (2)求证：ADAC.OAOC，AOC120，OCAOAC30又D30，DOCA，ADA能力培优6如下图，O是ABC的外接圆，FH是O的切线，切点为F，FHBC，连结AF交BC于E
5、，ABC的平分线BD交AF于D，连结BF.求证：(1)AF平分BAC；连接OF，则OFFH，BCFH，OFBC，BFFC，BAFCAF，即AF平分BAC(能力培优6如下图，O是ABC的外接圆，FH是O的切线，切点为F，FHBC，连结AF交BC于E，ABC的平分线BD交AF于D，连结BF.求证：(2)BFFD.FBCCAFBAF，DBEABD，又FBDFBCDBE，FDBABDBAF，FBDFDB，BFFD感谢聆听全文结束！再见全文结束！再见o study whether experiences during teen years would influence adult health.So
6、they followed 171 teens,starting when the kids were just 13.They interviewed each one every year for five years，and also spoke to these teens closest friends，who provided additional information about the quality of their friendships.The same 171 people were interviewed again at ages 25,26 and 27.Thi
7、s time,the questions surveyed each persons overall health.When the researchers analyzed the data,they found a strong connection between a teens behavior and adult health.Teens who had close friends grew up to be the healthier adults.Whether teens held back their feelings or expressed them to close f
8、riends also influenced later health.Those who held back their feelings were more likely to be sick as adults.The connection held up even after the scientists accounted for other possible influences on health.Weight，family income and drug use were all examined.So were mental health issues，such as anx
9、iety and depression.And in these people，such other factors did not explain adult health as well as teen friendships did.Getting along with the crowd may have benefits,says Allen,but there are also drawbacks.Teens who are more independent tend to do better at school and work.And peer pressure may lea
10、d some kids to engage in risky behavior,such as smoking,drinking or using drugs.Dealing with it is an ongoing challenge，Allen acknowledges.“Finding the right balance is the key.Teens shouldnt lose heart for not finding this easy.”And,he adds，“Parents need to be understanding about the pressures teens face.”
