# ГДЗ. Геометрия 10-11_Погорелов_2001_11кл_Решения пр20-23

• View
15.694

• Category

## Documents

Embed Size (px)

### Text of ГДЗ. Геометрия 10-11_Погорелов_2001_11кл_Решения пр20-23

3 11 . 10-11 .. , .: , 2001 .-4: 20 ................................................................ 4 21 ............................................................... 52 22 ............................................. 82 23 ..................... 1075 20. .1.- 1 2 . , 1=, 1=b1 11= 1. . 171, . 59.2. (b) -, b , (bc) - (,D1B1,,- BD , 1 ., BB1D1: BB1=B1D1tg60=4 3 (). CC1=BB1=4 3 ., 1A1 :A1C =10 100 ) 3 4 ( ) 52 (2 2 2121 1= = + = + CC C A ().: 10 .32., , 60.,ABD(AB=AD=a)BAD=60,ABD- BD = AB = a., BB1D B1D =22 2 212a a a BB BD = + = + . AD A=o120 cos 22 2 + DC AD DC AD == 32122 2 2a a a a = |.|

\| + . 1 :1=a a a CC AC 2 32 2 212= + = + .:2 a 2.2033. 5 , - 6 8 , 12. - .ABCD-=6,AD=8=12.-, 2AB2 + 2AD2 = AC2 + D2. :BD= = + 2 2 22 2 AC AD AB 56 12 8 2 6 22 2 2= + ()., 1 :1 = 2 2 2125 12 + = +CC AC =13().B1D B1D = ( )222125 56 + = + BB BD = 81 = 9().: 13 9 .34.1,-2311,2:3. .1=232=11d1d2,d1 : d2 = 2 : 3. d1 = 2k, d2 = 3k. , 2a12 + 222 = d12 + d22 , 2 232 + 2 112 = (2k)2 + (3k)2, 13k2 = 1300,k=10 (). d1 = 20() d2 = 30(). , h = 1 = 10 :S1 = d1 h = 20 10 = 200(2) = 2 (2).S2 = d2 h = 30 10 = 300(2) = 3 (2).: 22 32.2135. : 1) 1, 2, 2; 2) 2, 3, 6; 3) 6, 6, 7.,d2=a2 +b2 +c2.d = 2 2 2c b a + + :1) d =3 9 2 2 12 2 2= = + + ;2) d =7 49 6 3 22 2 2= = + + ;3) d =11 121 7 6 62 2 2= = + + .36.. , .A1D=2 a (1D).,1B1D-, A1B1 = a, A1D = 2 .,,1D2 = a2 + a2 + a2, B1D = a 3 A1B1D :S = 21A1B1 A1D =211 1D, A1H =323211 1 1aaa aD BD A B A==.: 32a .37. 7 24 , 8 . .1 = 7 2 = 24. :b=2 2 2 224 7 + = +b a = 25().22b = 25 = 8 (). :S = b c = 25 8 = 200(2) = 2(2).: 2 2.38. : 10 , 22 , 16 . = 10, b = 22 = 16 -.,. , :S = 2ab+2bc+2ac = 21022+22216+21016 = 1464 (2).: 1464 2.39.-,h,Q,- .AB = AD = b. BD :BD =2 2b a + . Q = AB AD = b.BB1D1D,=BDh,BD =h.: 22h= 2 + b2, Q = ab.:22h+ 2Q = 2 + b2 + 2ab, 22h+ 2Q = ( + b)2. : a + b =Qh222+ .23:S = P h = 2(a + b)h = 2hQh222+ = 22 22Qh + .40.,,,b. .,,z-. :x2 + 2 = 2.y2 + z2 = a2.z2 + x2 = b2. :22 = c2 + a2 - b2. = ) (212 2 2b a c + .:2z2 = a2 + b2 - c2, z =) (212 2 2b a c + 2x2 = b2 + c2- a2, x =) (212 2 2a c b + .41., 12 , 10 . -,- 45. .24SO- SK, SM SN AB. OK BC, ON AB.,SKO=SMO=SNO=45 .,SKO,SMOSNO . OK=OM=ON, -, . :S= = = ) 12 16 ( ) 10 16 ( ) 10 16 ( 16 ) )( )( ( BC p AC AB 48() , S = p r. r =1648=pS= 3 (). =r=3 . SOK 45, SOK SO=OK=3 .: 3 .42. 6 8 . 13 . .SA=SB=SC=SD,ASO, BSO, CSO DSO SO. AO = BO = CO = DO, , AC BD. ABD:BD=2 2 2 28 6 + = + AD AB =10(). OD =21BD = 5(). , SOD :SO =2 2 2 25 13 = OD SD = 12().: 12 .2543.; , . ?,SBC.SKBC.SMACSN AB. KN AB., SNK = SMK = .SMK=SNK.MK = NK. , MKC= NKB ( MK = NM = =60). = KB =2a., MK: = KC sin 60 = 43232 = . AK:K = AC sin 60 =23 a. SMK: SK = MK tg = 43 tg. SCK: tgSCK = = = tg2342 tg 3aaKCSK.SCK = SBK = arctg||.|

\| tg23. S:tgSAK = = = tg213 42 tg 3aaAKSK. SAK = arctg12tg|\

\| 2tg .59.ab:1);2);3) .SO-, ., AO = R. ASO:SO = 2 2 2 2R b AO AS = :1) R = 33 2., SO = 3 332222abab =||.|

\| .352) R = 22 a. SO = 2 222222abab =||.|

\| .3) R= a. SO = 2 2a b .60. b :1);2);3) .SO-,.SM.SM DC. OMDC. -, = r., SOM:SM = 2 2 2 2r b OM SO + = + . 1) r = 63 a. SM = 12 632222abab + =||.|

\|+ .2) r = 2a; SM =4 22222abab + = |.|

\|+ .3) r = 23 a; SM =43232222abab + =||.|

\|+3661.b- :1);2);3). SM = 2 2 2 2r b OM SO + = +( 60). S = S + S.n- , SM, S = n 21 a SM =21(na) SM =21P 2 2r b + , . 1) S = 432a r = 63 a. S =2 222124312321a ba ab a + = + . S =|.|

\|+ + = + +2 2 2 221243124343a b aaa ba a.2) S = a2 r = 2a. S = 2 22244421a b aab a + = + . S = a2 + a 2 24 a b +3) S = 6 23 3432 2a a=r = 23 a. S = 2 2223 42343621a ba ab a + = + . S =|.|

\|+ + = + +2 2 2 223 4 3233 42323 3a b aaa ba a.3762., , , - , r. - : =33 2r., :S = 6 3 293 464322 2rr AB= = ., SMB: = 3321r AB = , SB = a. :SM =322 2 2ra MB SB = .S= SM P 21,(SM).S= 2 2223 23 33 2621621r b rrbrSM AB = = . :S = 2r2) 3 3 ( 2 3 2 32 2 2 2r b r r r b r + = + .63.- 14,76 2, 18 2. - .38- . S = S S = 18 14,76 = 3,24(2) ABCD , A= Soc = 3 24 , = 1,8 (). S=21Ph,h,, h = SM = 8 , 1 476 , 14 242 2 ==ABSPS = 4,1 ()., SOM:SO =2 2 2 29 , 0 1 , 4 = OM SM = 4(), =21 = 0,9().: 1,8 4 .64. -,- .D ASC SO, , , - CD. AC = A 2 = a 2 .,-: 21AC SO = AD2 SO =222aa=a 2 ., SOM :SM = 4222 2 2aa OM SO + = + = 1,5a.S = 21 P SM, (SM ). S = 21 4a 1,5a = 3a2.: 32.3965. , - Q, .-, , S = cosQ.66. -,Q,- S. :S = cosQ. cos = SQ, = arccosSQ.67.- , 10 , 144 2. = = = x, SM = y . ASM : AS2 = AM2 + SM2, 102 =x24 + y 400 = x2 + 4y2.S = 21 P h, h , 144 = 21 3x y, xy = 96. :x yxy2 24 40096+ ==x2 + 4xy + 4y2 = 400 + 4 96;(x + 2y)2 = 784;40x + 2y = 28;x = 28 2y. 96 = (28 2y)y,96 = 28y 2y2,y2 14y + 48 = 0;y = 6 y = 8. x = 16 x = 12.: 16 6 12 8 .68.,5,16 2. = = D = AD = x, SM = y . - SMC:SC2 =SM2 + MC2 , 52 = y2 +x24, x2 + 4y2 = 100.S=S +S ,S, S = x2 S =21 P h, - h , S = 2xy. x2 + 2xy = 16.:x yx xy2 224 1002 16+ =+ =,y =1622 xx x2 + 416222|\

|.||xx= 100, x4 100x2 + (16 x2)2 = 0x4 66x2 + 128 = 0. x2 = a, a2 66a + 128 = 0,a = 2 a = 64. x = 2 = 8. = 8 . = 2 .:2 .69., . . 184, . 71.70. 7 . 10 2 . - .41 11, AA1=CC1 A1C1||AC. 11 .A11 ,- . ,11 = 11 2 = 2 2 () AC = A 2 =10 2().A1KACC1HAC111=1 = 7 . 1 1 - . =. = = 21( - 11) = 21(10 2 - 2 2 ) = 4 2(.), 1:AA1= ( ) 81 49 32 7 2 422212= + = + = + K A AK = 9 ().: 9 .71. - 4 1. 2 . . ., , 1- 111 .331ABR AO = =33 4= () 4233331 12 1 1= = =B AR O A ().11 . A1KAO. 11 , 11 = K =33 (). AK = AO KO =33333 4= ()., 1 :A1K =2 2 2 21) 3 ( 2 = AK AA=1().: 1 .72. 2 , 3 5 . .- 11. A11 , A1B1C1D1 ABCD, A11 = A11 2 = 3 2 () AC=A 2 = 5 2(c). A1KAC C1HAC. 11 11 = .,11 ., ==21( 11 ) =21(5 2 3 2 ) =2 . = = 5 2 2 = 4 2() 1:1 = 2 2 2 21) 2 4 ( 2 + = +CK K A = 6().: 6 .4373. - 2 6 . 60. . .,,1-, 111. SKAC, , SK1A1C1. OK1A1C1., O1K1 , - A A1B1C1. , = 63 663= AB=3() O1K1 = 3363 2631 1= = B A(). , K1HKO. K1O1OH , , 1 = 1K1KH,K1KH=60(-). 1:1 = tgK1KH =3 . = KO H = 11 =33 2333 =||.|

\| . 1 =33 23 = 2 ().1 = 1 = 2 : 2 .4474. , b. - 45. , .,,--,1,111 . A1O1 = R1 = 33 b AO = R2 =33 a.,A1KAO.A1O1OK, 1O1= . = = 33) (3333b ab a = ., 11 = 45. , A1K = AK = (a - b)33. A =23 a, A1B1C1: A1H1=23 b. 11 :S =33) (232321211 1b ab aK AH A AH ||.|

\|+ = +==332321 (a + b)(a b) =14(a2 b2).: 14(a2 b2).4575. 4 . 2 8. . , 4,,, 2 8 . - 2 2 8 2 . :S= 2 20 422 2 2 8= + (2).:2 20 .76.8,5,3. . .-,OO1 , 1 , - 111.1O1=33 5331 1=B A() O=33 833=AB().,.-, =3 423 823= =()

Recommended

Documents
Education
Education
Documents
Technology
Education
Education
Education
Education
Education
Education
Education