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1、.江蘇 1 衡水市 2019 高三上學(xué)期年末數(shù)學(xué)試題分類匯編-4-1選修 4-11、（常州市2013 屆高三期末）A選修 4 1：幾何證明選講如圖， AB 是 O 旳直徑， C,F 是 O上旳兩點(diǎn) ，OC AB ，過(guò)點(diǎn) F 作 O 旳切線 FD交 AB 旳延長(zhǎng)線于點(diǎn) D 連結(jié) CF 交AB于點(diǎn) E.C求證： DE 2DB DA.EBDAOFA選修 4 1：幾何證明選講證明：連結(jié)OF因?yàn)?DF切 O于 F，所以 OFD=90°C所以 OFC+ CFD=90°因?yàn)?OC=OF，所以 OCF= OFC因?yàn)?CO AB于 O，所以 OCF+ CEO=90° AEBDO所以

2、 CFD= CEO=DEF，所以 DF=DE2F因?yàn)?DF是 O旳切線 , 所以 DF=DB· DA2所以 DE=DB·DA2、（連云港市2013 屆高三期末）答案 ：.A.:FAD ABCDABC=CDF3AB=ACABC=ACB5ADB=ACBADB=CDF7 EDF=ADBEDF=CDF，ADCDF.1032013A.4 1OAB8,C,BC4,C,AAD,D,ADOE,AEAOC,BE,ACBEAEBC 4, OBOCBC4 ,OBC,CBOCOB604O C?DCA? CBO60oAD l? DAC90o -60o = 30o6OACACO1COB 30,2EAB

3、608Rt BAEEBA=30° AE1AB 410242013A4 1OOAABCADABCAEF ?BC1 ABACAE ADO2FAEFADBD CEF.(第 21A 題).1BEECABEADCRtABE ADCABAEADACAB ACAEAD52OFF?BAFCAFBC(1)BAECADFAEFAD1052013A4110ABOB,ADE , CFD , CGEOAC AB.FG / ACCGFODAEB第 21A 題圖AABAEAB2AD AEACABAD AEAC24ADACEACDAC ADC ACEACAEADCACEADCEGFEGFACEGFPAC106201

4、3A4 110OPABOACl l BDlDCDPCPDAPCABPCA·BO.（第 21-A 題）.72013A.10OBABCDP.A(1)=2=1APCCDPBABP?(2)POBPDPB=PD.OCDA.1·=·, =·2 =2×3,=.5PAPB PC PD AB CDABABAB3(2) OM CD M, ON AB NPOBPD OM=ON AB=CD,N7MCDABPONPOM PN=PM=.10PB PD82013A41:10ABO AC BAC AD O DDEAC AC EDEO.9、（鎮(zhèn)江市2013 屆高三期末）A（ 選

5、修 41幾何證明選講）如圖， O旳直徑 AB旳延長(zhǎng)線與弦CD旳延長(zhǎng)線相交于點(diǎn)P，E 為 O上一點(diǎn)， AE=AC， DE交AB于點(diǎn) 求證：FPDF POCEA·FBPODC（第 21-A 題）A 證明： AE=AC， CDE AOC，2 分又 CDE P+ PFD， AOC P+OCP，6 分從而 PFD OCP7 分在 PDF與 POC中， P P， PFD OCP，故 PDF POC10 分一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一

6、一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一

7、一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一.一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一一

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