北师大版数学总复习课后演练知能检测X412.doc
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1、(时间:60分钟,满分:80分)一、选择题(共6小题,每小题5分,满分30分)1已知:AD是O的直径,弦AB,AC交于A点且AD平分BAC,下列结论不正确的是()AABACB. ABCACADBC DABAC解析:AD为O对称轴且平分BAC,ABAC,ABAC ,B,C关于AD对称,则ADBC.故选D.答案:D2从不在O上的一点A作直线交O于B、C,且ABAC64,OA10,则O的半径等于()A2 B6C2 或6 D8或解析:设圆O的半径为r,当点在圆外时,由切割线定理得ABAC64(10r)(10r),解得r6;当点在圆内时,由相交弦定理得ABAC64(r10)(r10),解得r2.答案:C
2、3如图,ABC是O的内接正三角形,弦EF经过BC的中点D, 且EFAB,若AB2,则DE的长是A. B.C. D1解析:由题图知DEDFBDCD1,同理EGFG1.又DGAB1,DE(1FG)1,FG(1DE)1,DEFG.故选B.答案:B4如图,在圆内接四边形ABCD中,A60,B90,AB2,CD1,则BC()A2 B1C2 D22解析:延长BC交AD的延长线于P,B90,A60,P30,CDPB90.在RtCDP中,CD1,PC2.在RtABP中,BPAB2,BCBPPC22.答案:D5如图,AB、AC、CE都是O的切线,B、D、E为切点,P为上一点,若AC110,则BPE等于A70 B
3、60C55 D50解析:连接BD、DE,则ABDADB90A,CDECED90C,BDE180ADBCDE(AC)55,BPE55.故选C.答案:C6ABC是O的内接正三角形,弦EF经过BC的中点D,且EFAB,若AB2,则DE的长是()A. B.C. D1解析:由题图知DEDFBDCD1,同理EGFG1.又DGAB1,DE(1FG)1,FG(1DE)1,DEFG.故选B.答案:B二、填空题(共3小题,每小题5分,满分15分)7(2012年惠州模拟)如下图,EB、EC是O的两条切线,B、C是切点,A、D是O上两点,如果E46,DCF32,则A的度数是_解析:连接OB、OC、AC,根据弦切角定理
4、,可得ABACCAD(180E)DCF673299.答案:998(2011广东高考)如图,过圆O外一点P分别作圆的切线和割线交圆于A,B,且PB7,C是圆上一点使得BC5,BACAPB,则AB_.解析:由弦切角定理得PABACB,又因为BACAPB,所以PABACB,可得,将PB7,BC5代入得AB.答案:9(2011湖南高考)如图,A,E是半圆周上的两个三等分点,直径BC4,ADBC,垂足为D,BE与AD相交于点F,则AF的长为_解析:如图,连AE,易知AEBD,易知ABO是等边三角形,可得BD1,ADAFFD.AF.答案:三、解答题(共3小题,满分35分)10如图,AB是O的直径,D为O上
5、一点,过点D作O的切 线交AB的延长线于C,若DADC,求证:AB2BC.证明: 连接OD、BD,如图所示,因为AB是圆O的直径,所以ADB90,AB2OB因为DC是圆O的切线,所以CDO90.又因为DADC,所以AC,于是ADBCDO,从而ABCO.即2OBOBBC,得OBBC.故AB2BC.11(2011辽宁高考)如图,A,B,C,D四点在同一圆上,AD的延长线与BC的延长线交于E点,且ECED.(1)证明:CDAB;(2)延长CD到F,延长DC到G,使得EFEG,证明:A,B,G,F四点共圆证明:(1)因为ECED,所以EDCECD.因为A,B,C,D四点在同一圆上,所以EDCEBA.故
6、ECDEBA.所以CDAB.(2)由(1)知,AEBE.因为EFEG,故EFDEGC,从而FEDGEC.连结AF,BG,则EFAEGB,故FAEGBE.又 CDAB,EDCECD,所以FABGBA.所以AFGGBA180.故A,B,G,F四点共圆12如图,ABC的角平分线AD的延长线交它的外接圆于点E.(1)证明:ABEADC;(2)若ABC的面积SADAE,求BAC的大小解析:(1)证明:由已知条件,可得BAECAD.因为AEB与ACB是同弧上的圆周角,所以AEBACD.故ABEADC.(2)因为ABEADC,所以,即ABACADAE.又SABACsinBAC,且SADAE,故ABACsin
7、BACADAE.则sinBAC1,又BAC为三角形内角,所以BAC90. )来源:高考资源网版权所有:高考资源网(www.k s 5 ) 以下是大学体验英语综合教程2(第三版)课后翻译答案Unit11. 任何年满18岁的人都有资格投票。(be eligible to, vote)Answer:Anyone over the age of 18 is eligible to vote.2. 每学期开学前,这些奖学金的申请表格就会由学校发给每一个学生。(apply for, scholarship)Answer:A form to apply for these scholarships is s
8、ent by the university to every student before the start of every semester.3. 遵照医生的建议,我决定戒烟。(on the advice of)Answer:On the advice of my doctor, I decided to give up smoking.4. 公园位于县城的正中央。(be located in)Answer:The park is located right in the center of town.5. 这所大学提供了我们所需的所有材料和设备。(facilities)Answer:T
9、he university provides all the materials and facilities we desire.1. 他们花了多年的时间寻找内心的平静,但是收效甚微。(search for)Answer:They spent many years searching for peace of mind, but with little success.2. 这种新药的成功研制已经使许多疾病的治疗发生了根本性的变革。(revolutionize)Answer:The successful development of the new drug has revolutioniz
10、ed the treatment of many diseases.3. 由于这个国家的经济不景气,这家公司濒于破产。(on the edge of)Answer:The company is on the edge of bankruptcy due to the economic depression in the country.4. 大学毕业后他成为了一名护士。他认为护士这一职业可能很有发展前途。(rewarding)Answer:He became a nurse after college. He thought nursing could be a very rewarding
11、career.5. 他像往常一样在文件上签了名。(just as)Answer:He signed his name on the paper just as he has always done it.Unit21. 警察们正忙着填写关于这场事故的各种表格。(fill out)Answer:The policemen are busy fi lling out forms about the accident.2. 我想在还车之前把油箱加满。(fill up, fuel tank)Answer:I want to fi ll up the fuel tank before returning
12、 the car.3. 如果你要投诉,最好遵循正确的程序。(follow the procedure)Answer:If you want to make a complaint, youd better follow the correct procedure.4. 要不是约翰帮忙,我们绝不会这么快就完成实验。(without)Answer:We couldnt have fi nished the experiment so soon without Johns help.5. 暴风雨之后,岸边的人们焦急地搜索湖面以期发现小船的踪迹。(scan for)Answer:After the s
13、torm, the people on the shore anxiously scanned the lake for any sign of the boat.1. 这个国家不大,但是在国际事务中它却发挥着重要作用。(play a role)Answer:This country is not big, but it plays an important role in international affairs.2. 正是在我叔叔的帮助下,我得以克服困难,按时完成了任务。(it is . that)Answer:It was with the help of my uncle that
14、I overcame the difficulty and completed the assignment in time.3. 毕业时他决定留在北京,而他最好的朋友却选择了去西藏。(while)Answer:While he decided to stay in Beijing upon graduation, his best friend chose to go to Tibet.4. 在这次校园英语演讲比赛中,我们班的玛丽获得了第三名。(come in)Answer:In this Campus English Speaking Contest, Mary from our clas
15、s came in third.5. 你应该知道学习弹钢琴需要有时间,有金钱,还要有毅力。(as well as)Answer:You should know that it takes time, money as well as perseverance to learn to play the piano.Unit31. 我发现量入为出地过日子越来越难了。(increasingly)Answer:I find it increasingly difficult to live within my income.2. 现代政治家们都试图以电视讲话来影响普通百姓。(reach out)Ans
16、wer:Modern politicians try to reach out to ordinary people in their TV speeches.3. 应该帮助学生对人生采取积极的态度。(adopt)Answer:Pupils should be helped to adopt a positive attitude to life.4. 希望全班同学参加这些讨论。(participate in)Answer:Everyone in the class is expected to participate in these discussions.5. 如果你犯了罪就必须受到惩罚
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