直線和圓的位置關系典型習題

1、.直線和圓的位置關系典型習題1.如圖，AB為O的直徑，C為O上一點，AD和過點C的切線垂直于D， BE和過點C的切線垂直于E求證：（1）AC平分DAO（2）BC平分EBO（3）DC = CE（4）AD + BE = AB（5）ADCACB（6）CEBACBABCDEO（7）AC2 = AD·AB（8）BC2 = BE·AB2.已知：PA、PB分別切O于A、B，C為優(yōu)弧上一點，D為劣弧上一點。求證：（1）D = 90°+ P（2）C = 90° PPABCDAB3.如圖，兩個同心圓，大圓的弦AB和小圓相切，AB = a求證：圓環(huán)的面積 = 4.已知：AB為

2、O直徑，ADBC，B = 90°，DC切O于E求證：（1）CD = AD + BC（2）COD = 90°（3）OE2 = AD·BCOABCDEFG （4）連結AC、BD，交于點F，則EFBCABCDEO （5）延長EF交AB于G，則GF = EF5.RtABC中，B = 90°，AB = 6，BC = 8，則ABC的內(nèi)切圓半徑為_，ABC的外接圓半徑為_。ABPCDEO6.已知PA、PB分別切O于A、B，E為劣弧AB上一點，過E點的切線交PA于C、交PB于D。（1） 若PA = 6，求PCD的周長。（2） 若P = 50°求DOC7.已知圓

3、外切四邊形ABCD，則ABBCCDDA = 645_。（已知圓內(nèi)接四邊形ABCD，則ABCD = 234_）8.已知ABC中，AB=AC=13，ABC的面積為60，求ABC內(nèi)切圓直徑（此題兩個結果，可用相似求，也可利用S=C·r ）9.已知：如圖，PA、PB分別切O于A、B，AC為O直徑求證：（1）POBC（2）ABCPBO（3）PO·BC = 2OB2（ABPOCE4）（5）E為PAB的內(nèi)心DABCEI10.如右圖，點I是ABC的內(nèi)心，AI交邊BC于點D，交ABC的外接圓于點E。求證：（1）BE = IE（2）IE2 = DE·AE11、等邊三角形的邊長為，則它

4、的內(nèi)切圓半徑為_，外接圓半徑為_，高線為_。12、在ABC中，A的平分線AE交BC于D，交ABC的外接圓于E。（1）連結BE、CE，圖中有哪些相等的角？有哪些相等的線段？并證明：ADCBDEABEABDCEDAEC（2）過E作圓的切線MN，交AB的延長線于M，交AC的延長線于N，證明：MNBC（3）過B作圓的切線BF，證明：BE平分DBFDABCEFDABCEG（4）過A作圓的切線AG，交BC的延長線于G， 證明：AGD為等腰三角形。DABCEMNDABCE(1) (2) (3) (4)13、已知：AD切ABC的外接圓于A，交BC的延長線于D，DF平分ADB，分別交AC、AB于E、F。求證：（

5、1）DCDB = AC2AB2（2）AE = AFDABCEF（3）圖中共有多少組相似三角形（4）AE2 = CE·BE14、過O內(nèi)部或外部的一點P作O的割線，交O于A、B兩點。求證：PA·PB = OP2 r2（r為O的半徑）PPOABABO15、半徑為5的O中，半徑OC垂直于直徑AB，割線PC交O于D，交AB的延長線于P，若CD = 2，分別求PC、PB、BD的長（兩種方法：列方程，作OEPC于E）OABCPD16、已知：AB為O直徑，BAC = 20°，D為的中點， ED切O于D，求EDAABCDE17、延長O的直徑AB到P，使PB = OB，過P作PC切O

6、于C，過B作BD切O于B，交PC于D。OABPCD（1） 求P、A的度數(shù)（2） 求CDDP18.已知AB是O的直徑，BC是O的切線，切點為B，OCAD，（1）求證：DC是O的切線，（2）若O的半徑為R，求證：AD×OC=2 （3）若BC=6，O的半徑為3.求AD的長。（4）設OC交O于N，當AE：AO等于多少時，四邊形AOND菱形，請說明理由。 19.如圖ABC中，AB=AC，以AB為直徑的O交BC于D，DEAC于E，交BA的延長線于H。（1）求證：DE是O的切線，（2）若AH=，tanFBD=,求O的直徑。（3）試探究四邊形AEFG的形狀。BD，BA， BF三條線段之間的關系式，過

7、H作DHB的平分線交BC于M，當AB的長度變化時H在直線AB上的位置也發(fā)生變化，試問HMD的大小是否發(fā)生變化，若不發(fā)生變化，求出HMD的度數(shù)；若發(fā)生變化，請說明理由。（4）AH=，tanFBD= , 求BG的長度. 20.如圖以RtABC的直角邊AC為直徑的O交斜邊AB于D，過O作OEAB，交BC于E（1）求證：DE是O的切線，（2）CE=BE（3）如果O的半徑為，ED=2求AB的長。（4）當BAC為多少度時，AOED為平行四邊形？（5）在（4）的條件下，探索CODE的形狀。21.如圖AB=AC , ABC =,以AC為直徑作O，CO與O交于D，AD交BC于E，F(xiàn)是BE的中點，（1）判斷DF與

8、O的位置關系。（2）下列四個結論=CE×CB 4=ED×EA OCB=EAB DF=CD 其中正確結論是 （只填序號）并選擇一個證明22.已知點A，B，C，D在O上，DA=DC，AC，BD相交于E，DE=EB，延長BA至F，使AF=AB，連接DF（1）BD平分ABC（2）若DE=3，求AB的長 3試判斷DF與O的位置關系（4）求F的正弦值 （5）探索ABCD與BODC的形狀23、 如圖AB是O的直徑，AC=CE，CDAB于D，AE交CD于F，交BC于K。（1）求證：AF=CF （2）若tanECA=CD=2，求O的直徑 （3）連接OF，試判斷OF與BK之間的關系 （4）寫出

9、圖中至少三個不同的比例式或乘積式，并選擇一個證明。24.在ABC中AB=AC，O為AB的中點，以O為圓心，OB為半徑的圓交BC于D，過D作DEAC于E （1）求證：DE是O的切線 （2）若點O沿AB向點B運動，其它條件不變，那么DE與O有什么位置關系？并證明（3）若AB=AC=5，SinA=，那么圓心O在AB的什么位置時，O與AC相切？請說明理由8知ABC內(nèi)接于以AB為直徑的O過C作O的切線交AB的延長線于D，DA：AB=1：2 （1）求CDB的度數(shù) （2）在切線DC上截取CE=CD，連接EB，判斷EB與O有什么位置關系？并證明 （3）利用圖中已標明的字母，連接線段，指出至少5對相似三角形（不

10、包含全等，不需要證明）25如圖A為O的直徑EF上的一點，OB是和這條直徑垂直的半徑，BA和O相交于另一點C，過C的切線交EF的延長線于D，（1）求證：DA=DC AbxAC=AExAF (2)當DF：EF=1：8且DF=時，求ABxAC的值 （3）現(xiàn)將直徑EF所在的直線向上平移到如圖所示的位置其它條件不變，試猜想DA=DF是否仍然成立？26、如圖1，AB,AC分別為o的直徑和弦，D為的中點，過點D的切線與AC的延長線相交于點E。求證：DEAC； 求證：AD2=AE·AB；試判斷EA,EC,ED三條線段之間的數(shù)量關系，并證明；過點D作DFAB于F，如圖2， 求證：EC·EAA

11、F·BF； 27、如圖1，已知AB是o的直徑，延長AB到D，過D作o的切線DC，C為切點。求證：DC2=DA·DB；如圖2，求證：；若DC6，求AB的長；如圖3，過點C作CGAB于F，交o于G，若，BD=9,求 o的半徑及SinD； 28、已知：AB是o的直徑，BC是切線，切點為B，DC是o的切線。求證：OCAD； 若圓的半徑為R, 求證：AD·CO2R2；在的條件下，若OA2，ADOC6，求CD的長；延長 CD，BA相交于點E，若EA1，ED2，求tanEDA；若AD2,DC，求tanEDA；若AE3,CD:DE2：3，求 o的半徑；若BC6, o的半徑為3，求

12、AD的長；若ABBC2, 求ED:EC；29、如圖，在ABC中，以BC為直徑的O交AB于點F，E為AC上一點，EF是O的切線，E為AC的中點。1求證：AC是O的切線；2求證：AF·AB=4EF2 ；3連接OE，若四邊形OEFB是平行四邊形，求SinABE的值； 30、ABC是o的內(nèi)接三角形，弦AD平分BAC，交BC于點E 。求證：AB·ACAD·AE；求證：BD2DE·DA；求證：AD2BD2AB·AC；求證：AE2BE·ECAB·AC； 31、如圖，四邊形ABCD內(nèi)接于o，過點C的直線分別交AB、AD于F、H，AC平分BA

13、D，HFBD。求證：FH是o的切線；求證：BC2CE·CA；求證：CD2AB·DH；若I是ABD的內(nèi)心，試判斷CI、CE、CA之間的數(shù)量關系，并證明；32ABAC,以AB為直徑O交BC于點D，交AC于點E。1求證：DEBC。2已知AB5cm，DE3 cm，求BE的長。3過點D作DFAC,求證：F是CE的中點。4在的條件下，求證：BC24CF·CA。5若ABBC56,AE7,求CF的長。 33、已知ADBC,BCD900,以AB為直徑的O與DC相切于點E，交BC于F。1求證：AE平分BAD。2求證：AD+BC=AB。3求證：點E是DC的中點。4試判斷AD與FC的關系

14、，并證明。5求證：DC2=4AD·BC。6試判斷AD，AE,AB三條線段之間數(shù)量的關系，并證明。34、如圖，割線ABC與O相交于B,C兩點，D為O上一點，ACOE于F，DE交AC于G，ADG=AGD,1求證：AD是O的切線。2試探究線段AD,AB,AC之間的數(shù)量關系，并證明。3若AB=2,AD=4,EG=2, 求O的半徑。35、如圖BC為半園O的直徑，ADBC,=,BF和AD交于E。1求證：AB2=BE·BF。2求證：=。3連接OE,試判斷OE與MC的關系，并證明。 36、ABC是O的內(nèi)接三角形，D是的中點，延長DA,CB相交于點G。1求證：AB·ACAD

15、3;AG。2若AC為O的直徑，EAG1200,BC6,求AG的長。3在的條件下，求證：BC2DA·DG。37、已知，o的內(nèi)接四邊形是ABCD，對角線AC與BD互相垂直于點E。1連接AO并延長，交o于點F，求證：AB·ADAE·AF。2若AF與BD相交于點M，求證：AB·BFAC·BM。3過點O作ONAB于N，試判斷ON與CD之間的數(shù)量關系，并證明。 38、如圖，PA為O的切線，PBC為割線，APC的平分線交AB于E，交AC于F,交O于Q。(1) 求證；PAE=C。 （2）求證：AE=AF。(3)求證： = (4)求證：=內(nèi)部資料僅供參考9JWK

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31、MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5p

32、Dx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv

33、*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9C

34、pbK!zn%Mz849GxGjqvadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9C

35、pbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$v

36、STT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2

37、zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA

38、5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$

39、U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!z

40、n%MadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*adNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%

41、&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tn

42、GK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&

43、;ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA

44、5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYW

45、pazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*

46、3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjq

47、v$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&a

48、mp;gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm

49、6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pD

50、x2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&

51、qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z

52、89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%MzadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWF

53、A5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#

54、KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%

55、Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx

56、2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWF

57、A5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz84!z89Amv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&a

58、mp;qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U

59、E9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$U*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!

60、z89AmYWpazadNuGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWwcvR9CpbK!zn%Mz849GxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxGjqv$UE9wEwZ#QcUE%&qYpEh5pDx2zVkum&gTXRm6X4NGpP$vSTT#&ksv*3tnGK8!z89AmYWpazadNu#KN&MuWFA5uxY7JnD6YWRrWw