Геометрия7_9

KOJia p~iyca R, y HKOl 6it.IHi CTOpOHH - TBipHi KOHyca, a rocTpHH KYT npH HHmHi:H ocHoBi µ;opiBHIOe a. Paµ;iyc BB1 HHmHLo'iOCHOBH KOHyca 3HaXO,ZJ;HMO 3 npHMOKYTHOro TpHKYTHHKa

IlpH o6epTaHHi niBKpyra HaBKOJio µ;iaMeTpa AB HK oci, niBKpyr oIIHcye Kynro pa,ZJ;iyca R, HKHH µ;opiBHIOe pa,ZJ;iycy niBKpyra (Man. 339). IlpH n;1.0My nnocKHH KYT a onHcye KY.11.bOBUU ceKmop, a niBcerMeHT ADC Kpyra onHcye KY.11.bOBUU cez.M.enm, BHCOTa HKoro AD. ,n;yra AC niBKpyra onHcye cr/Jepu11.nuu cez.M.enm •

.n;nH BH3HatteHHH IIJIOIII; i o6'eMiB BHKOpHCTOBYIOTb TaKi cpopMYJIH.

n JW1l4-a c4Jepu paiJiyca R: s = 47tR2•

llAo~ c4Jepu11,noio cezMenmapaiJiycaR i Bucomu H: S=21tRH. 06'eM KyAi: V = ~1tR3 •

06'eM 1'Y/l.b06ozo ceKmopa: V = i1tR2 H, iJe H - Bucoma BiiJ-

noBiiJnozo c4Jepu11,nozo cez.Menma.

1.IIJ,o TaKe cTepeoMeTpiH?

2.CcpopMyJIIOHTe aKcioMH rpynH C.

3. .n;oBe,ZJ;iTb, w;o qepe3 TpH TO'IKH,HKi He nemaTb Ha O,ZJ;Hi:H npHMiH, MO:>K.Ha npoBeCTH IIJIOIIl;HHy.

4 . .n;oBe,ZJ;iTb, w;o KOJIH ,ZJ;Bi TO"IKH npHMOl HaJiemaTb IIJIOIIl;HHi, TO BCH npHMa HaJie:>K.HTb :u;i:H llJIOIIl;HHi.

5.HKi npHMi B npocTopi Ha3HBaIOTLCH napaneJILHHMH?

6.HKi npHMi Ha3HBaIOTLCH MHMo6imHHMH?

7.IIJ,o oaHattae: npHMa i nnom;HHa napanen1.Hi?

8.HKi nnom;HHH Ha3HBaIOTLCH napaneJILHHMH?

9.HKi npHMi B npocTopi Ha3HBaIOTLCH nepneH,ZJ;HKYJIHpHHMH?

10.,n;a:HTe 03HatteHHH nepneH,ZJ;HKYJIHpHOCTi npHMOl i IIJIOIIl;HHH.

11.IIJ,o Ha3HBaeTbCH Bi,ZJ;CTaHHIO Bi,ZJ; TO'IKH,ZJ;O IIJIOIIl;HHH?

12.IIJ,o TaKe npoeK:a;iH IIOXHJIOl?

13.HKi nnom;HHH Ha3HBaJOTLCH nepneH,ZJ;HKYJIJipHHMH?

14.IIJ,o TaKe ,ZJ;BorpaHHHH KYT?

15.IIJ;o TaKe npH3Ma; BHCOTa npH3MH?

16.SIR.a np11aua Ha3HBaE:TLCH npaBHJI1>H010?

17.IIJ;o TaKe napaJieJienine,A?

18.IIJ;o TaKe nipaM:i,Aa?

19.HKa nipaMi,Aa HaaHBaeTLCH npaBHJI1>Ho10?

20.IIoscHiTi., m;o TaKe apiaaHa nipaMi,Aa.

21.HaaBiTb HaiinpocTimi TiJia o6epTaHHH.

1.To~IKH A, B, C i D He JiemaTh B O,AHiH nJiow;uHi. ,D;oBe,AiT:&, w;o

nps:Mi AB i CD He nepeTHHaIOT:&CH.

2.qH MOmHa 'tlepeaTO"IKY nepeTHHY ,ABOX ,A8HHX IIpHMHX npoBecTH TpeTIO npHMY' .flKa He JiemHTb 3 HHMH B O,AHHi IIJIOm;HHi? IIoacHiT:& Bi,AnoBi,Ai..

3.qOTHpH TO"IKH He JiemaTb B O,AHHi UJIOm;HHi. qH MomyTb .HKiHe6y,Ab TPH 3 HHX JiemaTH Ha O,AHiH npaMiH? Ilo.HCHiTb Bi,AUO-

Bi,Ah.

4. ,D;oBe,AiT:&, m;o KOJIH nps:Mi AB i CD MHMo6imHi, TO npaMi AC .

i BD TaKom MHMo6imHi.

5.qepea Kim:i;i Bi,ApiaKa AB i H:oro cepe,AHHY M npoBe,AeHo napaJieJI:&Hi nps:Mi, m;o nepeTHHaIOT:& ,AeRKY nJiow;nHy B TO"IKax Ai.

2) AA1 = 3,6 ,AM, BB1 = 4,8 ,AM; 3) AA1 = 8,3 CM, BB1 = 4,1 CM;

4) AA1 =a, BB1 = b.

6.Ilpm.ri a Ta b He JiemaTb B O,AHHi IlJIOIIl;HHi. qH MomHa npouecTH npaMy c, napaJieJI:&Hy npRMHM a Tab?

7.,D;aHo TpHKYTHHK ABC. IlJiom;HHa, napaJieJI:&Ha np.HMiH: AB, nepeTHHae cTopoHy AC n;1>oro TpHKYTHHKa B To1:1n;i Ai. a cTo-

poHy BC - B To'ln;i B 1• 3Haii,AiTb ,AOBmHHY Bi,ApiaKa A1Bi. s:Kw;o: 1) AB = 15 cM, AA1 : AC = 2 : 3; 2) AB = 8 CM,

AA1 : A1C = 5 : 3; 3) B1C = 10 CM, AB : BC = 4 : 5; 4) AA1 = a,

AB= b,A1C = c.

8.,ll;oBe,AiTh, w;o KOJIH "IOTHpH npaMi, HKi npoXO,AHTb qepea TO"l-

KY A, nepeTHHaIOTb IlJIOIIl;HHY ex y BepmHHax napaJieJiorpaMa, TO BOHH nepeTHHaIOTb 6y,Ab-.flKY IIJIOm;HHY, napaJieJibHY ex, .flKa He npoxo,AHTb "lepea TO"IKY A, TaKom y uepmHHax napaJieJiorpaMa.

9. ,D;aHo TPH napaJieJILHi nJIOIIl;HHH cx1, cx2, cx3• HexaH: Xi. X2, Xa - TO"IKH .nepeTHHY IJ;HX IlJIOIIl;HH 3 ,AOBiJibHOIO npHMOIO. ,D;oBe,AiTL, m;o Bi,AHomeHHH ,AOBmHH Bi,ApiaKiB X 1X 2 : X 2X3 He aaJiemHTL Bi.A np.flMOl, T06To O,AHaKOBe ,AJI.H 6y,A:&-HKHX ,ABOX npRMHX.

10. llpHMi AB, AC i AD norrapHo rreprreHp;HR.YJISipHi. 3Haitp;iTb

Bi,ApiaoK CD, HKm;o: 1) AB = 3 cM, BC = 7 cM, AD = 1,5 cM;

2) BD = 9 CM, BC = 16 CM, AD = 5 cM; 3) AB = b, BC = a, AD = d; 4) BD = c, BC = a, AD = d.

§15. EJieMeHTH cTepeoMeTpil

11.'lJepe3n;eHTP OilHCaHoro HaBKOJl.O TpHKyrHHKa KOJia npoBe.n;eHO npsMy, nepneH,ZJ;HKYJIHPHY .n;o IlJIOID;HHH TpHKyrHHKa. ,D;oBe-

.n;iTL, m;o Ko:>fCHa TO'IKa n;iei: npHMOl piBHOBi.n;.n;aneHa Bi.n; Bep-

mHH TpHKYTHHKa.

12. 'lJepea BepmHHY A npHMOKYTHHKa ABCD npoBe.n;eHo npsMy AK, nepneH,ZJ;HKYJIHpHy 11.0 itoro nJioID;HHH. BiJJ,cTaHi Bi.n; TO'l- KH K lJ.O pemTH BepmHH npsMoKyrHHKa lJ,opiBHIOIOTL 6 M, 7 M

i 9 M. 3HaiilJ,iTL Bi.n;pi30K AK.

13.'lJepea TO'IKHA i B npoBe.n;eHo npsMi, nepneH,ZJ;HKYJIHpHi 11.0 nJIOID;HHH ex, HKi nepeTHHalOTL 11 Bi.n;noBi.n;Ho B TO'IKaxC i D.

3Hait.n;iTL Bi.n;cTaHL Mim TO'IKaMHA i B, HKID;O AC = 3 M, BD =

= 2 M, CD= 2,4 Mi Bi.n;piaoK AB He nepeTHHae nJIOID;HHY ex.

14.BepxHi KiHn;i ,Zl;BOX BepTHKaJILHHX CTOBiliB, HKi 3HaXO,ZJ;HTLCH Ha Bi.n;cTaHi 3,4 M o.n;HH Bi.n; o.n;Horo, a'e.n;HaHononepe'IKOJO. BH-

coTa O,D;HOro CTOBna 5,BM, a .zi;pyroro - 3,9M. 3Hait.zi;iTL ,ZJ;OBmHHY nonepe'IKH.

15.To'IKaA 3Haxo.n;HTLCH Ha Bi.n;cTaHi a Bi.n; BepmHH piBHOCTopoHHLoro TpHKYTHHKa ai CTOpOHOlO a. 3Hali.n;iTL Bi,ZJ;CTaHL Bi.n; TO'l- KH A .n;o nJIOIIJ;HHH TpHKyrHHKa.

16.Bi.n;cTaHi Bi.n; TO'IKH A .n;o BepmHH KBa,ZJ;paTa .n;opiBHlOJOTL a. 3Hait.n;iTL Bi,ZJ;CTaHL Bi.n; TO'IKHA .n;o IlJIOID;HHH KBa,ZJ;paTa, HKID;O CTOPOHa KBa,ZJ;paTa .n;opiBHlOe b.

17.3 TO'IOKA i B, HKi JiemaTL Ha rpaHsx ,n;BorpaHHoro KyTa,

onym;eHo nepneH,ZJ;HKYJIHpH AA1 i BB1 Ha pe6po KyTa. 3Hali-

.n;iTL: 1) .n;oBmHHY Bi.n;piaKa AB, HKID;O AA1 = a, BB1 = b, A1B1 = c i .n;BorpaHHHii KYT .n;opiBHlOe ex; 2) ,ZJ;BOrpaHHHH Kyr ex, HKID;O

AA1 = 3, BB1 = 4, A1B 1 = 6, AB= 7.

18. y npHMiH TpHKYTHiH npH3Mi CTOpOHH OCHOBH .n;opiBHlOlOTL 10 CM, 1 7 CM i 21 CM, a BHCOTa npH3MH 18 CM. 3Ha:H.n;iTL nJio- m;y nepepiay, npoBelJ,eHoro qepea 6i'IHepe6po i MeHmy BHCOTY OCHOBH.

19. y npaBHJILHiii 'IOTHpHKyrHiit'npH3Mi IlJIOID;a OCHOBH 144 CM2 , a BHCOTa 14 CM. 3Hali.n;iTL lJ,iaroHaJIL npH3MH.

npsMiH TpHKYTHiH npH3Mi Bci pe6pa piBHi. Bi'IHanoBepxHs

.n;opiBHlOe 12 M2 • 3Ha:H.n;iTL BHCOTY.

21. 3a CTOpOHOlO OCHOBH a i 6i'IHHMpe6pOM b 3Ha:H.n;iTL IlOBHY noBepXHlO npaBHJILHOl npH3MH: 1) TpHKYTHoi:; 2) 'IOTHPHKyrHoi:; 3) mecTHKYTHOL '

22.Y napaneJieninelJ,i TPH rpaHi MalOTL nJiom;i 1 M2 , 2 M2 i 3 M2 • 'lJoMy.n;opiBHlOe noBHa noBepxHH napaneJienine.n;a?

23.y npHMOMY napaJieJienine.n;i CTOpOHH OCHOBH 3 CM i 5 CM, a O,ZJ;Ha 3 .n;iarOHaJieH OCHOBH 4 CM. 3Hali.n;iTb 6iJILmy .n;iarOHaJib napaneJienine.n;a, 3HalO'IH, m;o MeHma .n;iaroHaJib yTBopioe a IlJIOID;HHOlO OCHOBH KYT 60°.

24.3Ha:H.n;iTL ,Zl;iaroHaJii npsMoro napaJieJienine.n;a, KOmHe pe6po HKOro .n;opi BHlOe a, a O,Zl;Hli 3 KyTiB OCHOBH .n;opiBHIOe 60°.

BHCOTY npaBHJILHOl nipaMi,ZJ;H: 1) TPHKYTHo'i;2) 'IOTHpHKyrHo1;

3) meCTHKYTHOL

32.BHcoTa npaBHJILHo1 'IOTHpHKYTHO'iapiaaao1 nipaMi,ZJ;H ,ZJ;opiBHIOe 4 CM. CTOpOHH OCHOB ,ZJ;opiBHIOIOTL 2 CM i 8 CM. 3HaH,ZJ;iTL IIJIO- m;i ,ZJ;iaroHaJILHHX rrepepiaiB.

33.TpH JiaTyHHHX Ky6H a pe6paMH 3 CM, 4 CM i 5 CM rrepenJiaBJieHO B O,ZJ;HH Ky6. .HKe pe6po n;Loro Ky6a?

34. .HKm;o KOmHe pe6po Ky6a a6iJILIDHTH Ha 1 M, TO H:oro o6'eM a6iJILIDHTLCH y 125 paa. 3HaH,ZJ;iTL pe6po.

35.BHMipH npHMOKYTHOro 6pycKa 3 CM, 4 CM i 5 CM. 51Km;o

a6iJILWHTH KOmHe pe6po Ha x CaHTHMeTpiB, TO IIOBepXHH 6pycKa a6iJILIDHTLCH Ha 54 cM2 • .HK a6iJILIDHTLCH iioro 06'eM?

36.y npHMOMY napaJieJienine,ZJ;i CTOPOHH OCHOBH 2 .J2 CM i 5 CM yTBopIOIOTL Kyr 45°. MeHma ,ZJ;iaroHaJIL napanenerrine,ZJ;a ,ZJ;opiB-

38.3a CTOpOHOIO OCHOBH a i 6i'IHHMpe6poM b aHait,ZJ;iTL o6'eMrrpaBHJILHOl rrpH3MH: 1) TPHKyrHo'i;2) 'IOTHpHKyrHol;3) mecTHKYTHol.

39.,ll;iaroHaJIL rrpaBHJILHOl 'IOTHpHKy>rHOlIIpH3MH ,ZJ;OpiBHIOe 3,5 CM, a ,ZJ;iaroHaJIL 6i'IHO'irpaHi 2,5 CM. 3HaH,ZJ;iTL o6'eMnpH3MH.

40.Ilepepia 3aJii3HWIHOro HaCHIIY Mae <t>opMy Tpanen;il, HHmHH OCHOBa HKOl 14 M, a BepXHH 8 M i BHCOTa 3,2 M. 3HaH,ZJ;iTL, CKiJILKH Ky6i'IHHXMeTpiB aeMJii IIpHIIa,ZJ;ae Ha 1 KM HaCHIIy.

41.3a CTOPOHOIO OCHOBH a i 6i11HHM pe6poM b 3Haitp;iTb o6'eMnpaBHJibHOl nipaMi,n:H: 1) TPHKyTHOl; 2) 'IOTHpHKyTHOi:;3) mecTHKyTHOL

42.Bit1Hi pe6pa TpHKyTHOl nipaMi,n:H BaaeMHo nepneH,ll;HKYJIHPHi i KmKHe ,n:opiBHIOe b. 3mm,n:iTb o6'eMnipaMi,n:H.

43.3Hd:,n:iTb o6'eMapiaaHOl nipaMi,ll;H 3 nJiom;aMH OCHOB Q1 i Q2 (Q1>Q2) i BHCOTOIO h.

44.qepea cepep;HHY BHCOTH nipaMi,ll;H npoBep;eHO llJIOID;HHy, napaJieJibHY OCHOBi. B .HKOMY Bi,z:i;HomeHHi BOHa ,z:i;iJIHTb o6'eMnipaMi,z:i;H?

45.Pa,z:i;iyc OCHOBH D;HJiiH,z:i;pa 2 M, BHCOTa 3 M. 3Ha:A,z:i;iTb ,z:i;iarOHaJib oc1>0Boro nepepiay.

46.BHCOTa D;HJiiH,z:i;pa 6 CM, pap;iyc OCHOBH 5 CM. 3Ha:A,ll;iTb nJiom;y

nepepiay, npoBe,n:eHoro napaneJibHO oci D;HJiiH,z:i;pa Ha Bip;cTaHi 4 CM Bi,IJ; HeL

47.Pa,z:i;iyc OCHOBH KOHyca 3M, BHCOTa 4 M. 3Ha:it,IJ;iTb TBipHy.

48.Pa,z:i;iyc ocHOBH KoHyca R. OcbOBHM nepepiaoM e np.HMOKYTHHH TpHKyTHHK. 3HaH:,z:i;iTb :itoro IIJiom;y.

49.KoHyc nepeTHyTO nJiom;HHOIO, napaneJibHOIO ocHoBi, Ha Bi,IJ;cTaHi d Bi,11; BepmHHH. 3Haii,z:i;iTb IIJiom;y nepepiay, .HKID;O pa,z:i;iyc ocHOBH KoHyca R, a BHCOTa H.

50.BHcoTa KoHyca H. Ha HKiii Bi,z:i;cTaHi Bi,z:i; BepmHHH Tpe6a npoBecTH IlJIOID;HHy, napaJieJibHY OCHOBi, m;o6 IIJiom;a nepepiay ,z:i;o- piBHIOBaJia IlOJIOBHHi nJiom;i OCHOBH?

51.Pa,z:i;iycH OCHOB apiaaHoro KOHyca 3 M i 6 M, BHCOTa 4 M. 3Haii- ,z:i;iTb TBipHy.

52.Pa,z:i;iycH OCHOB apiaaHoro KOHyca 3 ,ll;M i 7 )J;M, TBipHa 5 ,IJ;M. 3HaH:.n:iTb nJiom;y oc1>0Boro nepepiay.

53.KyJIIO pa,z:i;iyca R BIIHcaHo y apiaaHHii KoHyc. KyT HaXHJIY TBipHo'i.n:o IIJIOID;HHH HHmHbOl OCHOBH KOHyca ,z:i;opiBHIOe a. 3Hait-

.n:iTb pa,z:i;iycH OCHOB i TBipHy apiaaHoro KOHyca.

LE= t LC, L DBE= LB+ t (LA+ LC). 40. 140°, 10°. 41. 1) 20°;

§ 5.

1. BK a 3 i BK a. B~KJI~TL Ha npoMeHi B~piaoK, ~o p;opiBHIOE: pap;iy-

•cy. 2 . .ZJ;HB. 33.11,a11y 1. 5. 1) 60°; 2) 120°. 7. He Mome. 9. 30°. 10. 60° i

120°. 11. 70 CM, 10 CM. 12. He MO>KYTL. 13. 1) He MO>KyTL; 2) He MOmyTL. 14. 2) B K a 3 i B K a. CKopHcTaATecL p;ouep;eHHJIM B~ cynpoTHBHoro. 15. 2) BK a 3 i BK a. CKopncTMTeCL p;ouep;eHHSIM B~ cynpoTHBHoro;

3) BK a 3 i BK a. .ZJ;oue,D;iTL cno11aTKY'~o cniJILHa TO'IKa,D;aHHX Kin Jie- >KHTL Ha npaMiA, JIKa npoxop;HTL 11epe3 'ix ~eHTpH. 16. 2) B K a 3 i B K a. CKopHcTaftrecL p;ouep;eHHJIM B~ cynpoTHBHoro. 18. B K a 3 i B K a. CKopHcTaATecL TBepp;meHHJIM 33.11,a11i 16, 1). 28. BK a 3 i BK a. llo11HiTL 3 no6yp;oBH piBHOCTopoHHLoro TpHKYTHHKa. 32. BK a 3 i BK a. Y wyKaHoMy TPHKYTHHKY npop;oBmiTL Mep;iaHy aa li ,D;OB>KHHY. 36. B K a 3 i B -

6yp;yATe _cno11aTKY TpHKYTHHK, y JIKOro O,D;Ha CTOpOHa ,D;opiBHIO€ p;aai:A CTOpoHi myKaHoro TpHKYTHHKa, p;pyra CTOpoHa - cyMi ,!l;BOX iHWHX Aoro cropiH i KYT Mim HHMH p;opiBHIOE: p;aaoM:y KYTY· 47. BK a 3 i BK a. CKopHcTaATecL BKa3iBKOIO 11,0 nonepe11,aLo'i3ap;a11i 3 TieIO piaHH~eIO, ~o 3aMiCTL CYMH ,!l;BOX cropiH myKaHoro TpHKYTHHKa Tpe6a B3JITH lX pia- HH~IO. 48. .ZJ;HB. BKa3iBKY ,!l;O 3ap;a11i 46. 50. BK a 3 i BK a. 3uep;iTL

po3u'a3yuaaHJ13ap;a'Iip;o nonepe11,Hw'i,no6yp;yuaumH 11,onoMimae Kono, KOH~eHTPH'IHe 011,HOMY 3 ,D;aHHX, JIKe Mae pa.11,iyc, ~o p;opiBHIO€ cyMf

a6o piaHH~i pap;iyciB ,D;aHHX Kin.

§6.

3.Tpu. 4. 10 M:. 5. 3 CM i 4 CM. 7. BC =AD= 4,8 M. 8.AD = 15 CM, CD= 10 CM. 9. LB= L D = 150°, L c = 30°. 10. 3 CM. 11. 40°, 140°, 140°. 12. 115° i 65°. 13. He MO>KYTL. 14. 60°, 60°, 120°, 120°. 15. 1) 40°, 40°, 140°, 140°; 2) 50°, 50°, 130°, 130°; 3) 80°, 80°, 100°, 100°. 16.1) 55°,

32.lOCM i 25cM a6o 7,5cM i 18,75CM. 35. 80° i 100°. 37. 60° i 120°.

41.4 M. 43. 2 M. 44. 2 M. 45. 4 M, 8 M. 46. 1 M. 47. 10 CM. 50. 4 CM, 5 CM, 6cM. 51. 6cM. 52. 6cM, 5cM, 5cM. 56. 5M, 6M. 57. a+ b. 59. 3M, 4M.

61.70° i 110°. 62. l,7M. 63. 24cM, 36cM. 64. 60° i 120°. 65. 15M.

66.3cM. 67. 4M, 6M. 68. 2,2M. 69. gcM i 5cM. 70. a. 71. BKaaiBKa. IIo6y,!1;yATe cnoqaTKY TPHKYTHHK, ,ll;Bi CTOpOHH JIKoro ,ll;OpiBHIOIOTb 6iq-

HHM CTOPOHaM Tpanen;ii, a TpeTJI - piaHHD;i OCHOB. 72. BK a 3 i BK a. IIo6y,!1;yATe cnoqaTKY TPHKYTHHK, ,ll;Bi cTopoHH .11Koro ,ll;OpiBHIOIOTb Aiar0Ha.n.11M Tpanen;i'i,a TpeT.11 - cyMi 'iiocaoB. 73. IIo6y,!1;yAre cnoqaTKy

Bi,ll;piaoK x = a;. CKOpHCTaBWHCb poaB'.113KOM3a,ll;aqi 6.1.

§ 7.

2. 1) 5; 2) ..J2 "'1,4; 3) $1 "' 7,8. 3. 1) 4; 2) 12; 3) iii "'3,3. 4. 5 M a6o J7 M "'2,6 M. 5. He MO:>KYTb. 6. 1) 5 CM; 2) 17 ,ll;M; 3) 6,5 M.

Bi,ll;piaKOM i CKOpHCTaATeCb peayJibTRTOM 3a,ll;aqi 19. 22. CKOpHCTaATeCb peayJILTaToM aa,ll;aqi 21. 26. He Mome. 27. 2 M. 28. BKaaiBKa. Ilpo- ,ll;OBmiTb Me,ll;iaHy Ha iI ,ll;OB:>KHHy. 31. 2) BKaaiBKa. 3Be,ll;iTb poaB'.11ayBaHHJI n;iei 3a,ll;aqi ,ll;O nonepe,ll;HbOl Bi,ll;noBi,ll;Ho ,ll;O Ma.JIIOHKa 165, 6.

32. He MomyTb. 34. R - d, R + d. BK a a i BK a. CKopHcTaATecb aepiBHiCTIO TpHKYTHHKa. 35. d + R, d - R. B K a a i B K a. CKopHcTaATecb aepiBHicTIO TPHKYTHHKa. 36. He MO:>KYTb. 37. He MO:iKYTb. 38. BKaaiB-

=0,4163, cos 24°36'= 0,9092; 3) sin 70°32'= o,g428, cos 70°32'=

=0,3333; 4) sin 88°4g'= O,ggg8, cos 88°4g'= 0,0206. 50. 1) X = 1°;

52. 1) x = 17°53';2) x = 38°7';3) x = 80°46';4) x = 83°50'.53. 31°25';

31°25';117°10';23,8 M. 54. 34°10'i 55°50'. 55. 51°. 56. 116°16'i 63°44'. 57. 29°52'i 150°8'. 58. 12 M, 45°14'. 59. 60°16'. 60. Ji..

61. 1) a) 5; 36°52';53°8';6) 41; 12°41';77°19';B) 29; 43°36';46°24'; r) 61; 10°23';79°37';2) a) 12; 22°37';67°23';6) 24; 16°16';73°44';B) 15; 28°4';61°56';r) 13; 81°12';8°48';3) a) 70°; 0,68; 1,88; 6) 39°40';

3,08; 2,55; B) 19°24'; 7,55; 2,66; r) 13°39'; 15,55; 3, 78; 4) a) 59°33'; 5,92; 5,10; 6) 49°12'; 7,65; 5,79; B) 29°25'; 8,04; 3,95; r) 22°; 9,71;

§8.

3.2. 4. 3. 5. (2; 0). 6. (O; 3). 7. Ilp.HMa, napaJieJILHa oci y. 8. ,lJ;Bi

np.11Mi x = 3 i x = -3. 10. ,lJ;o~aTHy. 11. 4; 3. 12. 1) (3; 2); 2) (-1; 3);

3)(l; 1). 13. 1) (-2; 3); 2) (3; -5); 3) (-4.: 4). 16. (O; 1), (-2; 0), (-2; 1).

17.AB= 5, AC= 10, BC= 5. 18. To"IKa B. 20. (3; 3) i (15; 15).

~iTL TO"IKY nepeTHHY ~BOX np.RMHX i nepeBipTe, "IH Jie:>KHTh BOHa Ha Tpe-

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