Download - 立体几何复习课件 江苏省扬中高级中学
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( A B C D D
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1AA
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2Al Al
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3
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4
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5l1 // l2 , l1 ,l2 l1 //
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6ab,ab a
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L,L,( )A C B D
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A C B D L,L,( )
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L,L,( )A C B D D
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A0 B1 C2 D3
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A
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(1)(2)
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a b a//ba//ab(1) a,b=b(2) aaPP =b(3) a//b(4) a //
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,P-ABC,M,NPCAPBC,:MN//BCAPMN// EF MN //BCA
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,ABCDABEFAB,M.NAM=FN:MN//BCEABCDEFMNMN // GH MN //BCE
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ABCDEFMNAFN BNH AN/NH=FN/BN AN/NH=AM/MC MN//CH MN //BCE,ABCDABEFAB, M.NAM=FN:MN//BCE
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AC1EDD1DB1//A1C1EEDB1 // EF DB1 //A1C1E
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AC1OADD1A1CO // A1C1BB1O
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(1)(2)(3)
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a//,a, =ba//b =bb a //a b=a//b
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abc
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ala // a// =la // l
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abABOMNPa,bOABOa,bMNPMP=PN
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123
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42351
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123
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4.5.,a
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2. ,ABCD ABCDMP ABCD MP // .
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:,ABCD-A1B1C1D1 AB1D1BDC1B1D1AB1=B1AB1D1BDC1
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2A1CBDBDBC1=BA1CBDC1AB1D1BDC1
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1:ABCD-A1B1C1D1E,F,GA1D1,A1B1,A1A,EFGBDC12:OBDOC1 EFG
O EFGBDC1OC1 EFG
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3:,ABCD-A1B1C1D1 E,F,M,NA1B1,A1D1, B1C1, C1D1 AEFBDMN
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A-BCDE,F,GAB,AC,AD.EFGBCD
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(1)(2)1(3)2
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(1)(2)
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1l , m l____m2 n, m , mn_____, l m, l n, l 3l , m , l____m4l //m , l , m____ //
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PABCABOCABPAO1BCPAC
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PABC2)AHPC,AHPBCABOCABPAO
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OAC1,O,ACD1B1BD
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OHAC1OB1H D1O,B1HD1AC
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: l // ,m : l m m
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CAB PAABCPAABCPACABCPABABCBCPACPBCPAC
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l l
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l l
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ABCDADCBCDABD BCDDEBC ADE ABC ADCBCDABD BCDAD BCDAD BCDE BCBC ADEABC ADE
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ABC, ACB=90,PPA=PB=PC . PAB ABC
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ABCDAB=BCAD=CDEAC( (A) ABD BCD(B) BCD ABC(C) ACD ABC(D) ACD BDE
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ABCDPA ABCDPB,PC,PD,AC,BD,PACABCDPABABCDPADABCDPADPABPADPCDPBCPABPBDPAC
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P-ABCPBABCACB= 90,PB=BC=CA,EPC
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P-ABCDPAABCDBAD= 120,EPC
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:SABCASC=90ASB=BSC=60SA=SB=SCASCABC
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aboaba//ab//babab
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oabOooooo
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aboaba//ab//babab
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BA
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aboaba//ab//babab
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ABO
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aboaba//ab//bababALBO
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2.3.b.a.c. 1.
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AC1A1BB1CA1BB1C60A1B60
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AC1D1BB1CABDCA1B1D1C1
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AC1M,NA1AB1BCMD1NMN
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PABCMNP-ABCMNPBACPA=BC=4MN=3PABC
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1. AC1EGAA1CC1 FABC1EEFEFGD (A) 30 (B) 45 (C) 60(D) 90DM EB1EC1AB1EB1 EFDGAMEB1EF DG
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a,b50 PPa,b30 abPO2
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A1ABB1CDC1D1FEABG O1:ABCD-A1B1C1D1EFBB1 CDAED1F
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2ABCD-A' B'C' D', AB=BC=4, AA' =6, EFBB' CC', AEBF.
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3ABCD-A1B1C1D1AB=AA1=2 cm AD=1cmA1C1BD1
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BB1MO1MO1MD1BB1D1A1C1 O1A1O1MA1C1BD1O1M
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A1C1EA1C1BD1 A1EC1EA1C1EA1C1BD1()BC1B1F
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ABCDA1B1C1D1ACBC1 A30 B45 C60 D90
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SA BCEFSC A BEFSA A90 B60 C45 D30
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ACGEGFG EG//SA GEFEFSAFG//BCSABC EGF=90 EGFEG=SAFG=BC EG=FGEGF GEF=45C.
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ABCD- A1B1C1D1,ACBDO,OB1A1C11900
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S-ABCSABC, E, FSCAB EF SA CD(A)300 (B)450 (C)600 (D)9002B
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: a , M AB , N BB1 A1M C1 N EGABE, BE, BE A1M CC1G,BG. BG C1N EBGBG=BE= a, F C1 = acosEBG=2/5FEB1FNF,BENFFNCEBG
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11 2 1 cos 0 2 cos 0 3 cos = 0 3 90o2
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0 ]
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AB2AB 60
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C
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l160 9060Ol1
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l130 l2 l1 60 , l2 ?l1
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,OA,OCOAOB,AOC2:cos2= cos 1 cos
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,:(1)(2),
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:ABCD-A1B1C1D1A1BA1B1CDO
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SACBOFEACB=90SABC SCA= SCB= 60SCACB.
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SACBOFESA,SB,SCBSC=60,SAPBSC3, PSB,SC5,SABSCP
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ABCDFEADFDACA1BEABCD3AE=2BECF=2DFEFAEFDAGBCAEABCD
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ABCD-A1B1C1D1OACA1OBB1D1D.OO`
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PABCPAABCPABCD
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1.abab.______________.
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2.ABCDA1B1C1D1B1-AA1-C1_____B-AA1-D______C1-BD-C_______.4590
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3. -l-AB l 4530 ________________.45135
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B
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5. PAPBPCP60oB PAC ( )
A. B. C. D.AD
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ABCAMABCAMA ABCS ABCSA-BC-A.COS = S S
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AC1D1-AC-D
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ABCDASAABCDSBCSCDABCD45B-SC-D.E
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7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.
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7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.: (1)A1MABCA1M AA1C1C(1)AA1C1CABCBCACAA1C1CABC=ACBC AA1C1C
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7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.: (2)A1MABCAA1ABCA1AC,A1AC=60o,MACAA1C,CNAA1NNAA1,BNBC AA1C1CBCAA1AA1 BNCAA1 BN BNCB--AA1C
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7.ABCA1B1C1BCA=90AC=BCA1ABCACM. AA1ABC60.(1)BCAA1C1C(2)B-AA1-C.AC=BC=aAA1CaBNCBAA1C
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AC1EFABADC1-EF-CEFABDCA1B1D1C1H
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ABC,ABBC,SA ABC,DESC,SA=AB,SB=BC,E-BD-C?SABCED
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E
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P-ABCPA ABCPA=3AC=4PB=PC=BC. 1P-BC-A34H
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2A-PC-BCOS =P-ABCPA ABCPA=3AC=4PB=PC=BC. 1P-BC-A
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AC1E,F,A1ECFABCD.EF
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EFAC1E,F,A1ECFABCD.
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ABC-A1B1C12, (1) AB1A1C?(2)AB1BB1C1C?(3) DCC1,AB1DABC?
A1AB1C1BC
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ABC-A1B1C12, (1) AB1A1C?
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: A1A,AC, A1B1N,M, G,GN,NM.GNM.GM.GMGM=N
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1. ABC-A1B1C12, (1) AB1A1C?(2)AB1BB1C1C?E
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ABC-A1B1C12,(3) DCC1,AB1DABC?A1AB1C1BCD
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:AG
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A1AB1C1BCDM B1ABB1AMB.
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B1DBCM,AM
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CABDA1B1C1D1MN
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CABDA1B1C1D1MN
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CABDA1B1C1D1MN
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CABDA1B1C1D1MN
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CABDA1B1C1D1MN
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CABDA1B1C1D1MN
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B1A1C1 ABC ABCA1 B1 C1 BAC=90AB=BB1=1B1CABC30 BB1C AB B1CAB1CB1C
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C1 AA1B1BC
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1.(1)
(2)2.(1).(2).
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-AB-C
(AB)DCE
ABCEB( )
(A)CEBDEB (B)CEB=DEB
(C)CEBDEB
(D)CEBDEBA
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D
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112ABCDA1B1
C1D1BA1C1ABCD__
_____.arccos(1/3)
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5.ABCDACBDO
ABCDBD604
ACBDADCOAOC
BlBCDlAOC,
________
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6. PABCPCABC AB=BC=CA=PCBAPC EFBBEACEEEFPAFBFPCABCBEPACBFPABFEBPACPC=1 AB=BC=CA=PC=1EAC
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7.ABCDAB=BC=CD=aB=90DCB=135AC.(1)ABBCD(2)ABDACD.
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7.ABCDAB=BC=CD=aB=90DCB=135AC.(1)ABBCD(2)ABDACD.: (1)D-AC-B,DCAC,DCABC,()AB ABC,DCAB,ABBC,ABBCDABCD
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7.ABCDAB=BC=CD=aB=90DCB=135AC.(1)ABBCD(2)ABDACD.: (2)CCHDBH,ABDDCB,CHABD,ABBCDABD DCB=DB,BHHHEADE,ECE, CEADHEADCEADCEH ,CEH=60o, 60o
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().
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2lBBDDBClCCCDDCECEl BCElBCDl1BCD=45 BCE=13545135C.
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8.P1DCBP1DCBCDP1DP1D=6BC=3DC=3AP1D. ABP1ABPABP-CD-B45EFABPD.(1)AFPEC(2)P-BC-AEFP..:1PCG,.GFGEG,FG//CD,FG= CD,AE//CD,AE= CDAE//FG,AE=FG,AEGF,AF//EG,EG PEC,AF//PEC
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8.P1DCBP1DCBCDP1DP1D=6BC=3DC=3AP1D. ABP1ABPABP-CD-B45EFABPD.(1)AFPEC(2)P-BC-AP:2CDPAD,PADABCDPABP-BC-A,RtPAB,PA=3,PB= ,PA=AD,PDA=45o,PAADPAABCD,ABBC PBBCsinPBA=60o
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.
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9.ABCDA1B1C1D1EBCB1D1EABCD.ADBCB1A1D1C1.E:, ,.:B1C1M,.MEM,EBC,EMA1B1D1,B1D1 MD1B1E,B1D1EA1B1C1D1,ABCD//A1B1C1D1,B1D1EABCD, a,
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9.ABCDA1B1C1D1EBCB1D1EABCD.ADBCB1A1D1C1.F:BCF,.MBDEF,.EEBC,EF//BD,BD//B1D1,EF//B1D1,EFB1D1ABCDEB1D1F=EFBGEFFEG,GB1G,B1GBB1D1EABCD a,BE= BG= RtB1BG,B1G=
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ABC-A1B1C1MNAA1BB1B1N=A1B1=2A1MC1MNA1B1C1
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SABCSA=SB=SCASB=BSC=CSA=90MNABSCSMBN.Paaa
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1.1 2 3
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4 5 6
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2. 1 2 3
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ABCA1B1D1C1AC11,(1)ACD1D
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ABCA1B1D1C1AC11,(1)ACD1D(2)ABD1
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ABCDA1B1C1D1HAC1AB=aAA1=AD=bC1BDC1H=
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ABCDEFCDFEABFEEF=5,AD=13,ABCD
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P-ABCPA=PB=PCPABCPABCOOA=OB=OCOABC
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P-ABCPA,PB,PC,PABCPABCOABCDO
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P-ABCPABC,PABCPABCOABCOEF
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P-ABCPA=PB=PCPABCP-ABCPA,PB,PC,PABCP-ABCPABC,PABCPABCO
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ABCA1B1D1C1AC11,D(1)AA1B1CD
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ABCA1B1D1C1AC11,D(1)AA1B1CD(2)ABB1D1
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1PABCPABCABCOP
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4.PABCPAPBPCPAPBPC3PABC
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3.ABOPAOCAB5AC2BPAC
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PABCEFO
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ABEFDCPZ
3ABCD4EFABADPC
ABCDPC=2
1CPEFAPEF3
2BPEF
_1139904825.unknown
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l l AA`BB`l
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lA`AB
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ABCDA,B,C,DABCD4ABCD3
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5.ABCDABCDAA=5AB=12BCABCD
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ABCDPFEABCD4EFADABPCABCDPC=2BPEFGOH
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3ABCD4EFABADPCABCDPC=2BEFPACBDO,ACEFHOHPHBDPEFBBDOOKPEFOKKOKHPCH OK
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ABAB AABB
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:1 ,M,N,E,F .(1): ;(2): .
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1999ABCD-ABCDEDDEACDBEACABCD450AB=a1EAC2ABAC
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1600M--NPPMN12PaPAPBMNABPAPB,aQPQ=xPAQsinAQP=1/xRT PBQsin AQP=2/xcos600=cos(AQP +AQP)x
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2ABCDBAD=600AB=10PAABCDPA=51PCD2PBD3PAD4PCPAD(1)PCDCDEAEE(2)BDACOPOO
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1. ab ab d1 d2 ( )(A)d=d2 (B)dd2 (C)d1d2 (D)dd2DC
-
3. ABCAB=9AC=15BAC=120ABC
PABC14
P ( )
(A)7 (B)9 (C)11 (D)13A
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5.RtABCC ABAB=26ACBC45 30AB______.26.- l A l
2 , 1 ,
__________________30o 150o
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2.ABCDABACAD6BC3CD4BD5ABCDABD
-
7.MON=60POPO=3POMON45P
A.B. C. D.A8. EF ABCDEF
15AB17ABCD
28EFCD 2539
-
9. , AB, AB, A , B a b , abA a 2B b 5AB=4ab ababABAB
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ACDBA1B1D1C1O ACBDO AOBD AODD1 AOBD1 AO
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ACDBA1B1D1C1OEA1ACC1AB1D1 AA1CC1A1 CO1A A1EAO1E A1EAB1 D1 A1E
-
ACDBA1B1D1C1EF..A1CAB1D1 A1CBC1DA1CAB1D1BC1DEFEF
-
ACDBA1B1D1C1G.ABCDA1B1 BCDA1B1 BG(GBC1B1CBGB1C, BGCD BGA1B1CD :
-
(1)..
(2).
-
12. aABCDABC=60PCABCDEPAEPBC.:EPAEPBCA PBC.PCABCD,PBCABCDABCDAHBCBCH,AH= H
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12. aABCDABC=60PCABCDEPAEPBC.GO
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()
.
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PMN PM=3cm,PN=4cm,PMNlQ llQMlQNMQNlMQN=120M+N=180PMQNMPN=180120=60MN=
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()VSh
-
()
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(1) 1.(2)
-
(2)2.(3).(1)3.(1)....(2)abc l l2=a2+b2+c2
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VSh/3
-
()12
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PCBDARt PEHRt PHBRt PEBRt BEH
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1234
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1234PABC567
-
1.( )
(A)
(B)
(C)
(D)C
-
2.. ( )(A)0 (B)1 (C)3 (D)5C
-
2.ABC-A1B1C1AB=2 BB1AB1
C1B
A.60o B.90o C.105o D.75o
B
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3.a+b+c=611 __ 3045 ___ sinsinsin_____ ___________________________.sin2+sin2+sin2=2530
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8cm2,S=2
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,()
-
(
-
a.b,PABCO
-
1.60,PABCO
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1.60,PABDCO
-
a .60,30PABCO
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:P-ABC,AB=AC=10,BC=12,45,?
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aPABC
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a,hABDCOPHx
-
P-ABC4
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4. P-ABCDPAABCDABC=90PA=AB=BC=2AD=1, (1)DPBC (2)PABPCD: (1)AD//PBCDPBCAPBCPABC, ABBCBCPABPBCPABAPBAPBCPA=AB=2, PAAB,APBDPBC
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4. P-ABCDPAABCDABC=90PA=AB=BC=2AD=1, (1)DPBC (2)PABPCDQ (2)CDBAQ,ADBC, AD= BCAQB,PA=AB=AQBQPQ,BCPAB,CPPQ,CPB,PCDPCD
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1P-ABCDaPBABCD.(1)PADABCD600 PBABCDBAADPAADPABPADABCDPAB600
-
1P-ABCDaPBABCD.(2)PBPADPCD900.MPADPCDCMPDMMACDMADMAMCMAMD900AMC.ACAMCcosAMC =AMC900.
-
P-ABCDaBCD600PBABCD.PADABCD600E
-
P-ABCDaBCD600PBCABCDPBC. PADABCDE
-
2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2 (1)DE
-
2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2(2)A-BD-C() ABC-A1B1C1ACBCACBB1C1CCMBDMAMAMCACMAC2ACCM
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3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (1)A1BABD()BGEBG
-
3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDAB
-
3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDADEAA1B1BADEAA1B1BAEA
-
3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDBC
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1234
-
C1.8cm2
()( )
(A)4cm2 (B) cm2 (C)2cm2 (D) cm22. ( ) (A)1 : 4 (B) 1 : 3 (C) 1 : 8 (D) 1 : 7 C
-
A3.a,b,c
245 2
( )
(A) (B) (C) (D)
-
C4.S
a ( )
(A) (B) (C) (D)5.2340P-ABCAPBPCEFAEF ( )
(A) 6 (B) (C) 36 (D) A
-
PP A B C D
-
ABCDAAOPPAPBPCPD Ph1h2h3h4ABCD
-
6.A1B1C1ABCABCAB=AC=10cmBC=12cmA1ABCAA1=13cm.BBDAA1DCDDAA1=A1B=A1CABCA1ABCOBCAEOEBCAA1,B1BCC1AA1BCAA1BDAA1BDC,AA1CDA1ABA1FABFFRtA1FAA1A=13AF=5A1F=12,BD=ABsinA1AB=10S=(BD+DC+BC)A1A=396,ABCAEBCAB=10BE=6,AE=8,SABC=8,S=396+248=492(cm) 2
-
7.EFaABCDA1B1C1D1A1ACC1C1B1EDF....FE::A1C1, B1D1O1,O1O1O1H B1DH,HEF//A1C1, A1C1//B1EDF C1B1EDF A1C1 B1EDFB1D1DB1EDF,O1HB1EDF O1H B1O1HB1DD1
-
7.EFaABCDA1B1C1D1A1ACC1C1B1EDF...FE::EFB1C1EFh1,DC1EFh2 , h1+h2=B1D1=2a ,
-
7.EFaABCDA1B1C1D1A1ACC1C1B1EDF...FE::
-
aABCDACBDaD-ABCABCD
-
aABCDACBDaD-ABCABCD
-
ABCD-A1B1C1D1EFBB1DD1a,D1-AEC1FEF
-
,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1A1B1C1D1ABCD
-
A1B1C1D1ABCD,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1
-
2A1B1C1D1ABCDV= SA1B1CD1CE,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1
-
A1B1C1D1ABCDSB1CD1=2,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1
-
A1B1C1D1ABCDSB1CD1=V= ( 2 SB1C1D1)h2,AB=AD=2aAA1=a A1AD= A1AB= DAB= 601AA1B1CD1
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a.
-
18 3
-
SQ
-
PABCP-ABCPA=a, PB=b, PC=c , ABCSPABC
-
ABCDPFE:ABCD4,E,FADABPCABCDPC=2BPEFGOH
-
ABCDPFEG:ABCD4,E,FADABPCABCDPC=2BPEF
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ABC-A`B`C`BB`C`CSAA`a
-
ABCA`B`C`ABC-A`B`C`BB`C`CSAA`a
-
,ABCDEF,ABCD3,EF//AB,EF=1.5, EFAC2,=4.5=3
-
=6=1.5,ABCDEF,ABCD3,EF//AB,EF=1.5, EFAC2,
-
ABC-A1B1C134ABB1C1
-
43
-
43
-
P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60
-
P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60
-
P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60
-
P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60
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P-ABCPA=1AB=AC=2 PAB= PAC= BAC= 60
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:S ABC,EFSBSC AEFSCB.SABC SOAOBCD SDEFGAG.
GO
-
ABCSD1
-
ABCSEFKEY
-
aABCD-A1B1C1D1D1C1BDABCDA1B1C1D1 = KEY
-
ABCDA1B1C1D1AD=AA1=1AB=2EABD1EA1DEAB,EACD1AED1ECD
-
PBCDEAPABCD PBADPAD2ABCDPADABCD120PABCDAPBCPB,,..
-
18 cm2,3cm.,OABCOODBCABACDEDEDEF VBCABVACVDFEF
-
AGV= AOF=600
-
D
-
C
-
4. ( ) (A)1 : 4 (B) 1 : 3 (C) 1 : 8 (D) 1 : 7 C
-
A
-
C
-
A
-
8. ABCDEAEABCBDAEAC=AB=BC=BD=2AE=1FCD(1)EFBCD(2)ABCDE(3)CDEABDE..
-
9.P-ABCPAPBPC60PA=aPB=bPC=cP-ABC.
-
10.A1B1C1ABCABCAB=AC=10cmBC=12cmA1ABCAA1=13cm..BCDAA1.E
-
1.2.1/3.
-
3012 A5400 B6480 C7200 D7920 E+2=V+F
-
.
-
AC3.45o
90o
______
-
C4. 2 A. 2 B.2 C.22 D.45.2_____________6.PABCOPAPBPC
PA=PB=PC=a, OABC
______________
-
7.ABCFDE aAEF BFDF ABEADE BFAEDFAE, BFDB-AE-D BDFBF=DE= BD= - arccos
-
A-BCDAB=CD=6,5 .ECDEAEBECDAECDBECDABEAD=5,DE=3AE=BE=4ABE37VA-BCD=VC-ABE+VD-ABE12 rVA-BCD= (SABC+SBCD+SCDA+SDAB)r= 48r =16r 16r=67
-
.
-
OO2O1
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9.14cm 64cm2 36cm2.R111R2-36-R2-64=14 222R2-36 +R2-64=14 R=10 S=4R2=400(cm)2
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14
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14
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HO
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R
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MMAMBMCMABC2MAMBMC MAMBMCd=4MA2+MB2+MC2=d2=16.
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RMAMBMC.(1)MA2+MB2+MC2(2)M-ABC.(1)MAMBMC..MA2+MB2+MC2=4R2..
(2).
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1..2. !
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AA2.VF( ) (A)2F+V=4 (B)2F-V=4 (C)2F+V=2 (D)2F-V=2
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A3.2030.( ) (A)2160 (B)5400 (C)6480 (D)7200A4.31( ) (A)16 (B)17 (C)18 (D)19
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A
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BCAD ABD ACD1BDCD2 BAC=60.ABCD
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EFABCDBCCDAEEFAFABE ECFAFDBCDP, 1AP EF 2A-EF-P
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1APPFAP PE PEPE=P APPEF EF PEF AP EF.
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2EFHPHAHPE=PFAE=AF AH EFPH EF AHPA-EF-P(1)AP PEFPH PEFAP PH APHRt.
cosAHP= AHP=arcos A-EF-Parcos
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ABCDAB=3BC=4BDA-BD-CABCDBC 1ABCD 2 ABCD
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3RtABCAB=3BC=4EACBEABEA-BE-CACABE
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1ABCD-A1B1C1D1AB=3BC=2AA1=1AC1 A B C D
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2
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5.BMEDCNBECNBM60DMBN
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1,,,
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2,,
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ABCDFD ( )
B
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ABCD-A1B1C1D1__________()
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.P1P2P3. ( )(A)P3P2P1(B)P3P2=P1(C)P3=P2P1(D)P3=P2=P1 D
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CH44(4).4cos ( )(A)-1/3 (B)1/3(C)-1/2 (D)1/2A
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xoyABCD(50)(-30)(0-4)(-4-3)y.(1)ADBC(2)BCODEEFADFEFADBCEF(3)C-AOD.ADBC.
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1121223 33.12
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200243.1234
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5.()P-ABCPPAPBPCP1P2P3(())P1P2=P2P3.(1)P-ABCPABC.(2)P1P2=26P1P3=20P-ABC.
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1P-ABCDaPBABCD.(1)PADABCD600 PBABCDBAADPAADPABPADABCDPAB600
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1P-ABCDaPBABCD.(2)PBPADPCD900.MPADPCDCMPDMMACDMADMAMCMAMD900AMC.ACAMCcosAMC =AMC900.
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P-ABCDaBCD600PBABCD.PADABCD600E
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P-ABCDaBCD600PBCABCDPBC. PADABCDE
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2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2 (1)DE
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2ABC-A1B1C1ABCRt C=900 DECC1A1BAC=AA1=2(2)A-BD-C() ABC-A1B1C1ACBCACBB1C1CCMBDMAMAMCACMAC2ACCM
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3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (1)A1BABD()BGEBG
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3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDAB
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3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDADEAA1B1BADEAA1B1BAEA
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3ABC-A1B1C1ABCRtC=900 DECC1A1BAA12EABDABDG. (2)A1AEDBC
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2DA1C1B1DAA1C1CAB1DAA1C1CA1A1GADADGA1GAB1DA1A1HAB1HHGAB1HGA1HGA1B1AD
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ABCDA1B1C1D1A1B1C1D1AC1AEC1FABCD
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ABCA1B1C1AB1BC1AB=CC1=aBC=b1EFAB1BC1 EF//ABC2A1C1AB3B1ABC1.
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1EFAB1BC1EF//ABC
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2A1C1AB2A1B ABCA1B1C1 AA1ABAB=CC1=AA1 ABB1A1AB1BA1 AB1BC1 AB1A1BC1 A1C1AB1A1C1AA1 A1C1ABB1A1 A1C1AB
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3B1ABC1. 3 A1B1//AB A1B1//ABC B1ABC1A1ABC1 A1A1HAC1H2 BAACC1A1
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B1ABC1
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aABCD-A1B1C1D1EFABBC(1)B-FB1-E(2)DB1EF(3)DD1MBMEFB.M.B1EFDD1M.B1BDD1B1EFB1BDD1B1EF=B1GB1BDD1BMB1GDD1MBMB1EFB1BGBDMMDD1M...
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M
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BC
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05PABCABBCABBCkPAODACPCOPABC()k PAPBC() kOPBCPBC
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P-ABCPACABC PA=PB=PC=3 1AB BC 2AB=BC= ACPBC . 2004EF
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PADPCDACPBAMCBMC 1.0518P-ABCDABDC ABCDPA=AD=DC= AB=1MPB
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3D-AB-EABCD2AEEBFCEBFACEAEBCEB-AC-EDACE
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PABCDABCDPAABCDAB= BC=1PA=2EPD.ACPBPABNNEPACNABAP.