I. Burchaklar

III. Uchburchaklar.

1. Uchburchakning ikkita burchaklarining qiymatini nisbati 1:2 kabi. Uchinchi burchak shu burchaklarning kichigidan 40⁰ ga katta.Uchburchakning katta burchagini toping.
(96–7–36)
A) 102⁰ B) 93⁰ C) 75⁰ D) 80⁰ E) 105⁰
2. Uchburchak ikkita burchakning qiymatlari nisbati 3:4 kabi, uchinchisiniki shu burchaklarning kattasidan 4⁰ ga katta. Uchburchakning katta burchagini toping. (97–3–36)
A) 84⁰ B) 68⁰ C) 96⁰ D) 64⁰ E) 72⁰
3. Aagar uchburchakning A,B,C burchaklari 1,2 va 3 sonlarga proporsional bo`lsa, B burchakni toping. (97–5–43)
A) 30⁰ B) 60⁰ C) 90⁰ D) 45⁰ E) 120⁰
4. Uchburchak burchaklarning kattaliklari 2;3 va 10 sonlariga proporsional. Uchburchakning burchaklarini toping. (99–6–3)
A)24⁰;36⁰;120⁰ B)20⁰;46⁰;120⁰ C)10⁰;30⁰;120⁰ D) 30⁰;40⁰;110⁰ E) 60⁰;90⁰;10⁰
5. Uchburburchak ikkita burchagining qiymatlari 5:9 kabi. Uchinchi burchagi shu burchaklarning kichigidan 10⁰ ga kichik. Uchburchakning eng kichik burchagini toping. (97–7–36)
A) 30⁰ B) 40⁰ C) 45⁰ D) 50⁰ E) 20⁰
6. Uchburchak ikkita burchaklarining kattaliklari nisbati 3:2 ga teng. Uchinchi burchagi chu burchaklarning kattasidan 60⁰ ga kichik. Uchburchakni kichik burchagini toping.
(97–10–36)
A) 50⁰ B) 45⁰ C) 40⁰ D) 30⁰ E) 15⁰
7. 108⁰ li tashqi burchagiga qo`shni bo`lmagan ichki burchaklarning nisbati 5:4 kabi. Shu ichki burchaklarning kichigini toping. (00–3–73)
A) 40⁰ B) 45⁰ C) 72⁰ D) 48⁰ E) 30⁰
8. Uchburchakning ikkita tashqi burchaklari 120⁰ va 160⁰ ga teng. Uning uchinchi tashqi burchagini toping. (00–6–34)
A) 100⁰ B) 80⁰ C) 90⁰ D) 70⁰ E) 60⁰
9. Teng yonli uchburchakning yon tomoniga tushirilgan balangligi bilan ikkinchi yon tomoni orasidagi burchak 20⁰ ga teng. Teng yonli uchburchakning asosidagi burchagini toping.
(97–1–28)
A) 50⁰ B) 48⁰ C) 55⁰ D) 58⁰ E) 65⁰
10. Teng yonli uchburchakning uchidagi burchagi 94⁰. Asosidagi burchaklarning bissektrissalari kesishsishidan hosil bo`lgan o`tkir burchakni toping. (97–6–28)
A)37⁰ B)43⁰ C)48⁰ D)47⁰ E)aniqlab bo`lmaydi.
11. Teng yonli uchburchakning uchidagi burchagi 80⁰ ga teng. Yon tomonga o`tkazilgan balandlik va asosi orasidagi burchakni toping. (97–8–18)
A) 35⁰ B) 45⁰ C) 30⁰ D) 40⁰ E) 50⁰
12. Teng yonli uchburchakning uchidagi burchagi 30⁰ ga teng. Uning yon tomoniga tushirilgan balandligi bilan asosi orasidagi burchakni toping. (99–4–37)
A) 75⁰ B) 15⁰ C) 20⁰ D) 45⁰ E) 65⁰
13. Teng yonli uchburchakning asosidagiburchagi 30 ga teng. Shu uchburchakni yon tomoni va ikkinchi yon tomoniga tushirilgan balandlik orasidagi burchakni toping. (00–6–36)
A) 75⁰ B) 60⁰ C) 45⁰ D) 40⁰ E) 30⁰
14. Teng yonli uchburchakning asosidagi burchagi 40⁰ ga teng. Bu uchburchakning yon tomonlari orasidagi burchakka qo`shni bo`lgan tashqi burchakning qiymatini toping. (98–11–81)
A) 90⁰ B) 100⁰ C) 140⁰ D) 50⁰ E) 80⁰
15. Teng yonli uchburchakning yon tomoni 38,6 ga, asosiga tushirilgan balandligi esa 19,3 ga teng. Asosidagi burchaklarning bissektrissalari kesishishidan hosil bo`lgan o`tmas burchakni toping. (97–11–28)
A) 110⁰ B) 120⁰ C) 135⁰ D) 140⁰ E) 150⁰
16. Teng yonli uchburchakning uchidagi tashqi burchagi o`sha uchidagi ichki burchagidan 4 marta katta. Uchburchakning tashqi burchagi necha gradus? (97–2–18)
A) 100 B) 102 C) 96 D) 108 E) 104
17. Teng yonli ABC uchburchakda AC–asos, CD – C burchakning bissektrissasi va ADC=150⁰, B ning kattaligini toping. (00–6–37)
A) 140⁰ B) 120⁰ C) 110⁰ D) 80⁰ E) 60⁰
18. ABC uchburchakda A uchidagi tashqi burchagi 120⁰ ga, C uchidagi ichki burchagi 80⁰ ga teng. B uchidagi tashqi burchagini toping. (96–6–18)
A) 160⁰ B) 150⁰ C) 130⁰ D) 120⁰ E)140⁰
19. Uchburchakning ikkita tashqi burchagini yig`indisi 240<sup>0</sup> ga teng. Uning shu burchaklariga qo`shni bo`lmagan ichki burchagini toping.
(98–2–45)
A) 30⁰ B) 45⁰ C) 90⁰ D) 75⁰ E) 60⁰
20. Burchakning bissektrissasi uning tomoni bilan 15⁰ li burchak tashkil etsa , burchakning o`zini toping. (97–5–41)
A) 45⁰ B) 30⁰ C) 60⁰ D) 90⁰ E) 7,5⁰
21. Burchakning bissektrissasi uning tomoni bilan 45⁰ li burchak tashkil etsa , burchakning o`zini toping. (97–9–41)
A) 22,5⁰ B) 90⁰ C) 60⁰ D) 15⁰ E) 35⁰
22. Agar uchburchakning burchaklari 5;6 va 7 sonlariga proporsional bo`lsa, uchburchakning katta burchagini toping. (97–9–43)
A) 75⁰ B) 80⁰ C) 50⁰ D) 40⁰ E) 70⁰
23. Uchburchakning yuzi 6 ga teng. Shu uchburchakning 3 va 8 ga teng tomonlari orasidagi burchakni toping. (97–12–37)
A) 30⁰ B) 45⁰ C) 60⁰ D) 60⁰ yoki 120⁰
E) 30⁰ yoki 150⁰
24. Teng yonli uchburchakning perimetri 10 ga teng. yon tomoni aosisdan 12 marta uzun uchburchakning asosi qanchaga teng? (00–8–23)
A) 0,4 B) 0,8 C) 0,5 D) 0,6 E) 0,7
25. Teng yonli ABC uchburchakda A= C, AB:AC=5:3 va AB–AC=3 ga teng. Uchburchakning perimetrini toping. (00–5–54)
A) 19,5 B) 18,5 C) 17,5 D) 16 E) 15
26. A va B nuqtalar orasidagi masofa 500 m ga, B va C nuqtalari orasidagi masofa esa 300 m ga teng. A va C nuqatalar orasidagi masofa qanchaga teng.
(98–4–26)
A)1300 B)800 C)200 D)700 E)aniqlab bo`lmaydi
27. a (- ) ning qanday qiymatlarida uzunliklari mos ravishda 1+a, 1–2a va 2 ga teng bo`lgan kesmalardan uchburchak yasash mumkin.
(96–3–97)
A)(–1;0) B) (0; ) C) (– ;0)
D) (– ; ) E) (– ;0)
28. a ning qanday qiymatida uzunliklari mos ravishda 1+2a, 1–a va 2 ga teng bo`lgan kesmlardan uchburchak yasash mumkin? (96–9–33)
A)Ø B)(– ;0) C)(0; ) D)(– ;0) E)(– ;1)
29. a ning qanday qiymatida uzunliklari mos ravishda 1+4a, 1–a va 2a ga teng bo`lgan kesmalardan uchburchak yasash mumkin? (96–12–99)
A)(– ;0) B)(0;1) C)Ø D)(– ;0) E)(– ;0)
30. a ning qanday qiymatlarida uzunliklari mos ravishda 1+a, 1–a va 1,5 bo`lgan kesmalardan uchburchak yasash mumkin? (96–13–39)
A)(–0,75;0,75) B)(–0,5;0,5) C) Ǿ
D) (–0,7;0,7) E) (–0,4;0,4)
31. Uzunligi 1;3;5;7;9 ga teng bo`lgan kesmalar berilgan.Bu kesmalardan tomonlari har xil bo`lgan nechta turli uchburchak yasash mumkin.
(98–4–42)
A) 4 B) 3 C) 5 D) 2 E) 6
32. Uchburchakning ikkita tomoni 0,8 va 1,9 ga teng. Uchinchi tomoni uzunligi butun son ekanligini bilgan holda shu tomonni toping. (97–7–64)
A) 1 B) 2 C) 3 D) 4
E) bunday tomon mavjud emas
33. Uchburchakning ikkita tomoni 0,5 va 7,9 ga teng. Uchinchi tomoni uzunligi butun son ekanligini bilgan holda shu tomonni toping. (97–9–57)
A) 8 B) 7 C) 6 D) 5 E) 4
34. Uchburchakning birinchi tomoni x (x>5) sm, ikkinchi tomoni undan 3 sm qisqa, uchinchi tomoni esa birinchisidan 2 sm uzun. Shu uchburchakning perimetrini (sm) toping. (96–3–17)
A) 3x+1 B) 3x+5 C) 3x–1
D) 3x+2 E) 3x–3
35. Uchburchakning birinchi tomoni x (x>7) sm, ikkinchi tomoni undan 4 sm qisqa, uchinchi tomoni esa birinchisidan 3 sm uzun. Shu uchburchakning perimetrini (sm) toping. (96–11–18)
A) 3x–1 B) 3x+4 C) 3x–3
D) 3x+7 E) 3x–4
36. Uchburchakning birinchi tomoni x(x>5) sm, ikkinchi tomoni undan 2 sm qisqa, uchinchi tomoni esa birinchisidan 3 sm uzun. Shu uchburchakning perimetrini (sm) toping.
(96–12–18)
A) 3x–1 B) 3x+2 C) 3x–2
D) 3x+3 E) 3x+1
37. Agar uchburchakning tomonlari butun sonlar bo`lib, uning perimetri 15 ga teng bo`lsa, quyidagilardan qaysilari uning tomonlari bo`la olmaydi? (00–8–66)
A) 3;5;7 B) 4;4;7 C) 4;5;6; D)3;4;8
E) 3;5;7 yoki 4;5;6
38. Uchburchakning a va b tomonlari orasidagi burchak α ga teng. Uchburchak yuzasi quyidagi ifodalardan qaysi biriga teng. (96–1–47)
A) ab•sinα B) C)
D) 2ab•cosα E) ab•cosα
39. To`g`ri burchakli uchburchak kateti 8 sm. Uning gipotenuzadagi proyeksiyasi esa 6,4 sm. Shu uchburchakning yuzasi necha sm² ? (96–1–38)
A) 25,6 B) 48 C) 51,2 D) 24 E) 18
40. To`g`ri burchakli uchburchak gipotenuzasi 50 sm. Katta ketetning gipotenuzadagi proyeksiyasi 32 sm. Shu uchburchakning yuzasi necha sm² ?
(96–9–89)
A) 1200 B) 576 C) 300 D) 600 E) 800
41. To`g`ri burchakli uchburchak gipotenuzasi 10 sm. Kichik ketetning gipotenuzadagi proyeksiyasi esa 3,6 sm. Shu uchburchakning yuzasi necha sm² ?
(96–10–40)
A) 48 B) 24 C) 18 D) 32 E) 20,4
42. Katetlarning nisbati 2:3 kabi bo`lgan to`g`ri burchakli uchburchak gipotenuzasi 13 ga teng. Uchburchakning yuzini toping. (97–3–38)
A) 5 B) 24 C) 39 D) 36 E) 6
43. Katetlardan biri 8 ga teng bo`lgan to`g`ri burchakli uchburchak gipotenuzasining ikkinchi katetga nisbati 5:3 ga teng. Uchburchakning yuzini toping. (97–7–38)
A) 12 B) 15 C) 20 D) 24 E) 48
44. To`g`ri burchakli uchburchakning katetlari 5:6 kabi nisbatda, gipotenuzasi esa 122 ga teng. Gipotenuzaning balandlik kesib ajratgan kesmalarini toping. (96–7–45)
A) 45 va 72 B) 42 va 80 C) 50 va 72
D) 32 va 90 E) 60 va 62
45. To`g`ri burchakli uchburchakning gipotenuzasi 25 sm, katetlari o`zaro 3:4 nisbatda. Shu uchburchakning kichik katetini toping. (96–1–40)
A) 10 B) 12 C) 9 D) 15 E) 20
46. Katetlarining nisbati 3:2 kabi bo`lgan to`g`ri burchakli uchburchakning balandligi gipotenuzasini uzunliklaridan biri ikkinchisidan 2 ga ko`p bo`lgan qismlarga ajratadi. Berilgan uchburchakning gipotenuzasini toping. (97–3–45)
A) 5,2 B) 4,8 C) 6 D) 8 E) 7,6
47. Katetlarining nisbati 2:3 kabi bo`lgab to`g`ri burchakli uchburchakning balandligi gipotenuzasini uzunliklaridan biri ikkinchisidan 2 ga kam bo`lgan qismlarga ajratadi. Gipotenuzani bo`laklarini toping. (97–10–45)
A) 2 va 4 B) 5 va 3 C) 0,9 va 3,9
D) 1,6 va 3,6 E) 2,8 va 4,8
48. Gipotenuzasi 50 ga teng bo`lgan to`g`ri burchakli uchburchakning katetlari nisbati 4:3 ga teng. Gipotenuzaga tushirilgan balandlik uni qanday kesmalarga ajratadi? (97–7–45)
A) 20 va 30 B) 15 va 35 C) 18 va 32
D) 12 va 38 E) 14 va 36
49. To`g`ri burchakli uchburchak to`g`ri burchagining bissektrisasi gipotenuzani 1:2 nisbatda bo`ladi. Uchburchak balandligi gipotenuzani qanday nisbatda bo`ladi? (97–5–54)
A) 2:1 B) 1:2 C) 3:1 D) 1:3 E) 1:4
50. To`g`ri burchakli uchburchak to`g`ri burchakning bissektrisasi gipotenuzani 1:5 nisbatda bo`ladi. Uchburchakning balandligi gipotenuzani qanday nisbatda bo`ladi? (97–9–54)
A) 25:1 B) 1:25 C) 1:5 D) 5:1 E) 1:6
51. To`g`ri buchakli uchburchakning kateti 7 ga, uning gipotenuzaga proyeksiyasi 1,96 ga teng. Ikkinchi katetning uzunligini toping. (97–6–32)
A) 12 B) 16 C) 24 D) 15 E) 26
52. To`g`ri burchaklning katetlari 15 va 20 ga teng. Katta katetning gipotenuzadagi proyeksiyasini toping. (97–1–32)
A) 12 B) 14,5 C) 16 D) 16,5 E) 18
53. To`g`ri burchakli uchburchakning bitta kateti 2 ga, bu katet qarshisidagi burchak 60⁰ ga teng. Ikkinchi katetni toping. (97–9–49)

54. To`g`ri burchakli uchburchakning katetlari 24 va 7 ga teng. Kichik katetning gipotenuzadagi proyeksiyasini toping. (97–11–32)

55. To`g`ri burchakli uchburchakning gipotenuzasi 25 ga , katetlaridan biri 10 ga teng.Ikkinchi katetning gipotenuzadagi proyeksiyasini toping. (98–1–38)
A) 14 B) 15,5 C) 18 D) 20,4 E) 21
56. To`g`ri burchakli uchburchakning gipotenuzasi 6 ga, katetlaridan biri 4 ga teng.Shu katetning gipotenuzadagi proyeksiyasini toping. (98–5–34)

57. To`g`ri burchakli uchburchakning katetlari 9 va 12 ga teng. kichik katetning gipotenuzadagi proyeksiyasini toping. (98–8–38)

58. To`g`ri burchakli uchburchakning katetlari 4 va 6 ga teng. Shu uchburchakning to`g`ri burchagidan chiqarilgan bissektrisasini uzunligini toping.
(00–6–41)

59. CB=5, CD=1,6. AB²=? (98–3–36)

60. CD=3, DB=12. AD=? (98–10–83)

61. Rasmda C=90⁰ , CD AB, CA=6 va AB=10, AD ning uzunligini toping. (97–2–26)

62. (96–3–44) h–?

63. AC=10 sm, AD=6 sm ,AB–? sm (96–9–34)

64. AC=5 sm, AD=3sm , AB–? sm (96–12–54)

65. h–? (96–13–35)

66. To`g`ri burchakli uchburchakning katetlaridan biri 12, gipotenuzasi esa ikkinchi katetdan 6 ga ortiq. Uchburchakning yuzini toping.(96–7–38)
A) 36 B) 54 C) 40 D) 60 E) 42
67. To`g`ri burchakli uchburchak katetlaridan biri 12 sm, ikkinchisi esa gipotenuzadan 8 sm qisqa. Shu uchburchak gipotenuzasini toping. (96–9–91)
A) 15 B) 16 C) 25 D) 13 E) 29
68. To`g`ri burchakli uchburchakning gipotenuzasi 8 ga, katetlaridan biri 4 ga teng. Ikkinchi katetning gipotenuzadagi proyeksiyasini toping. (99–7–34)
A) 4 B) 3 C) 5 D) 7 E) 6
69. To`g`ri burchakli uchburchak katetlaridan biri 12 sm, gipotenuzasi esa ikkinchi katetdan 6 sm uzun. Gipotenuzani uzunligini toping. (96–10–42)
A) 15 B) 25 C) 26 D) 18 E) 32
70. Uchburchakning katetlaridan biri 6 ga teng, ikkinchisi gipotenuzadan 2 ga kam. Uchburchakning yuzini toping. (97–10–38)
A) 24 B) 18 C) 15 D) 12 E) 30
71. To`g`ri burchakli uchburchak katetlarining gipote4nuzadagi proyeksiyalari 8 va 2 ga teng. Uchburchakning yuzini toping. (99–8–51)
A) 10 B) 20 C) 40 D) 24 E) 16
72. To`g`ri burchakli uchburchakning gipotenuzasi 13 ga, katetlaridan biri ga teng. Gipotenuzaga tushirilgan balandlikni uzunligini toping. (98–7–46)
A) 5 B) 6 C) 7 D) 4 E) 9
73. To`g`ri burchakli uchburchakning balandligi gipotenuzani 2 va 18 ga teng bo`lgan kesmalarga ajratadi. Shu balandlikni toping. (98–6–34)
A) 4 B) 5 C) 12 D) 6 E) 6
74. Teng yonli to`g`ri burchakli uchburchakning yuzi 1225 ga teng bo`lsa, uning gipotenuzasini toping. (00–8–49)
A) 70 B) 65 C) 72 D) 49 E) 50
75. To`g`ri burchakli uchburchakning kateti 2 ga, bu katet qarshisidagi burchak 60⁰ ga teng. Shu uchburchak gipotenuzasini toping. (97–5–49)

76. To`g`ri burchakli uchburchakning o`tkir burchagi 60⁰, gipotenuzasiga tushirilgan balandligi 9 ga teng. Berilgan uchburchakning gipotenuzasini toping. (98–11–82)

77. ∆ABC da B=90⁰, C=60⁰. BB₁ balandlik 2 ga teng. AB ning toping. (99–1–31)
A) 4 B) 2 C) 2 D) 2 E)
78. To`g`ri burchakli uchburchakning gipotenuzasi 13 ga, gioptenuzaga tushirilgan balandligi 6 ga teng. Katta katetning gipotenuzadagi proyeksiyasini toping. (98–12–46)
A) 9 B) 4 C) 5 D) 25 E) 7
79. To`g`ri burchakli uchburchakda to`gri burchak bissektrisasi gipotenuzani 3:2 nisbatda bo`lgan kesmalarga ajratadi. Katetlarning gipotenuzadagi proyeksiyalari nisbatini toping. (99–8–44)

80. To`g`ri burchakli uchburchakning burchaklaridan biri 60⁰ ga, gioptenuzaga tushirilgan medianasi 15 ga teng. Kichik katetning uzunligini toping.
(98–10–28)
A) 7,5 B) 10,5 C) 15 D) 12 E) 20
81. Gipotenuzasi c ga va o`tkir burchaklari sinuslarining yig`indisi q ga teng bo`lgan to`g`ri burchakli uchburchakning yuzini toping.
(00–10–76)
A) с²(q²–1) B) q²(c²–1) C) q ²(c²+1)
D) с²(q²+1) E) q²(1–c²)
82. To`g`ri burchakli uchburchak gipotenuzasining shu gipotenuzaga tushirilgan medianaga nisbatini toping. (97–4–45)
A) 3 B) 4 C) 2,5 D) 2 E) 1,5
83. Agar teng yonli to`g`ri burchakli uchburchakning yuzasi 18 ga teng bo`lsa, gipotenuzaning uzunligi qanchaga teng bo`ladi? (98–11–36)
A) 6 B) 2 C) 2 D) 6 E) 6
84. Teng yonli to`g`ri burchakli uchburchakning gipotenuzasi 5 ga teng. Uning yuzini hisoblang. (00–10–31)
A) 14,5 B) 12,5 C) 10,5 D) 8,5 E) 16,5
85. Teng yonli uchburchakning 15 ga teng. Yon tomoni asosidan 15 ga kam. Shu uchburchakning asosini toping. (97–1–29)
A) 20 B) 40 C) 30 D) 24 E) 32
86. Teng yonli uchburchakning balandligi 4 ga, asosi 6 ga teng. Uning yon tomoni toping. (97–5–45)
A) 5,5 B) 7 C) 5 D) 9 E) 4,5
87. Teng yonli uchburchakning asosi 48 ga, unga tushirilgan balandlig 7 ga teng. Uchburchakning yon tomonini toping. (97–9–45)
A) 25 B) 27 C) 18 D) 19 E) 15
88. Teng yonli uchburchakning yon yomoni 25 ga teng. Asosiga tushirilgan balandligi asosidan 25 ga kam. Shu uchburchakning asosini toping.
(97–11–29)
A) 44 B) 30 C) 35 D) 40 E) 48
89. Balandligi 6 ga teng bo`lgan, teng yonli uchburchakning asosi yon yomonidan 6 ga ortiq. Uchburchakning asosini toping. (97–6–29)
A) 16 B) 15 C) 18 D) 24 E) 20
90. Teng yonli uchburchakning perimetri 14 ga teng. Asosi yon tomonidan uch marta kichik. Uchburchak yuzini toping. (98–1–40)
A) 4 B) 8 C) D) 12 E) 2
91. Teng yonli uchburchakning asosi 18, yuzi 108 ga teng. Shu uchburchakning yon tomonini toping.
(98–8–40)
A) 15 B) 16 C) 12,5 D) 21 E) 25
92. Muntazam uchburchakning yuzi 25 ga teng. Uning tomonini toping. (98–2–48)
A) 15 B) 20 C) 10 D) 12 E) 8
93. Muntazam uchburchakning yuzi 64 ga teng. Uning perimetrini toping. (00–4–48)
A)16 B) C)64 D)64 E)
94. Muntazam uchburchakning ichidagi ixtiyoriy nuqtadan uning tomonlarigacha bo`lgan masofalar yig`indisi ga teng .Uchburchakning yuzini toping. (98–4–28)
A) 4 B) 3 C) D)
E) aniqlab bo`lmaydi
95. Tomoni ga teng bo`lgan muntazam uchburchakning ichidagi ixtiyoriy nuqtadan uning tomonlarigacha bo`lgan masofalar yig`indisi qanchaga teng bo`ladi ? (98–12–86)
A) 3 B) 1,5 C) D)nuqtaning vaziyatiga bog`liq E)
96. Tomonlari 13;14 va 15 sm bo`lgan uchburchakning eng kichik balandligi necha sm? (96–3–104)
A) 11,2 B) 11,1 C) 11 D) 11,5 E) 11,6
97. ABC uchburchakda A=30⁰, AB= , AC=4. A uchdan tushirilgan balandlik uzunligini toping.
(98–3–38)

98. ∆ABC da BAC=45⁰ , ACB=30⁰, BC=14 ga teng. AB tomoni uzunligini toping. (98–10–48)
A) 12 B) 15 C) 14 D) 12 E) 12
99. ABC uchburchakda A=30⁰, AB= , AC=6. A uchidan tushirilgan balandligining uzunligini toping. (98–10–85)

100. ABC uchburchakda AB=5 sm, AC=10 sm va A=45⁰. Shu uchburchakning yuzi necha sm² ? (96–3–47)

101. ABC uchburchakda AB=4 sm, AC=5 sm va A=45⁰. Shu uchburchakning yuzi necha sm² ? (96–11–48)

102. ABC uchburchakda AB=3 sm, AC=6 sm va A=45⁰. Shu uchburchakning yuzi necha sm² ? (96–12–50)

103. Uchburchakning tomonlari 4; 5 va 6 sm. 4sm li tomonining 6 smli tomonidagi proyeksiyasi necha sm ? (96–3–39)

104. Uchburchakning tomonlari 7; 5 va 6 sm. 5sm li tomonining 7 smli tomonidagi proyeksiyasi necha sm ? (96–11–40)

105. Uchburchakning tomonlari 4; 5 va 6 m. 5 m li tomonining 6 m li tomonidagi proyeksiyasi necha sm? (96–12–41)

106. Uchburchak burchaklarining kattaliklari nisbati 1:1:2 kabi, katta tomonining uzunligi esa 13 ga teng.Uchburchakning katta tomoniga tushirilgan balandlikni toping. (97–1–33)
A) 6,5 B) 12 C) 8 D) 5 E) 10
107. Kichik tomoni ga teng bo`lgan uchburchakning burchaklari 1:2:3 kabi nisbatda bo`lsa, uchburchakning perimetrini toping.
(97–1–69)
A) 8+3 B) 3(2+ ) C) 11
D) 9+4 E) 6+6
108. Uchburchak burchaklarining nisbati 2:3:1 kabi; tomonining uzunligi 5 ga teng. Uchburchakning katta tomnonini uzunligini toping. (97–6–33)
A) 13 B) 25 C) 10 D) 5 E) 12
109. Uchburchak burchaklarining qiymatlari 1:2:3 nisbatda, katta tomoni ga teng. Uchburchakning perimetrini toping. (97–6–73)
A) 8+3 B) 3(2+ ) C) 11
D) 9+4 E) 6+6
110. Burchaklarining kattalaiklari nisbati 9:5:4 kabi bo`lgan uchburchakning katta tomoniga tushirilgan medianasi 12,5 ga teng. Uchburchakning katta tomonini toping.
(97–11–33)
A) 20 B) 16 C) 25 D) 32 E) 26
111. ABC uchburchakning BC tomoniga AD to`g`ri chiziq shunday tushirilganki, CAD= ACD, ABC va ABD uchburchaklarning perimetrlari mos ravishda 37 va 24 ga teng. AC tomonining uzunligini toping. (99–4–35)
A) 6,5 B) 13 C) 10 D) 7 E) 5
112. ABC uchburchakning C uchidagi tashqi burchagi 90⁰ ga teng. Agar CA=12 va CB=5 bo`lsa, AB tomonga tushirilgan CD mediananing uzunligini toping. (00–7–42)
A) 6 B) 6,5 C) 5 D) 5,5 E) 7
113. Medianalari 9;12 va 15 ga teng uchburchakning yuzini toping. (00–10–61)
A) 50 B) 48 C) 75 D) 49 E) 72
114. ABC uchburchakning BD, AE va CF medianalari O nuqtada kesishadi. ∆AOD ning yuzi 2,8 ga teng. ∆BFC ning yuzini toping. (00–9–51)

115. Rasmdagi ABC uchburchakda AB=8 va AD=2 bo`lsa, ABC va DBE uchburchaklar yuzlarining nisbatini toping (AC||DE). (97–4–54)

116. Rasmda MN||AC. MBN uchburchakning perimetri 42 sm, ABC uchburchakning perimetri 84 sm, MBN uchburchakning yuzi 27 sm². ABC uchburchakning yuzini (sm²) toping. (97–12–38)

117. Rasmda DEB=60⁰, BE=3 va DE=2 (uchburchakning o`rta chizig`i) bo`lsa, AB ni toping (98–5–35)

118. Rasmda muntazam ABC uchburchakning perimetri 3 ga teng. Agar AB₁=2AB va AC₁=2AC bo`lsa, AB₁C₁ uchburchakning perimetrini toping. (97–4–48)

119. Rasmdagi ABCD kvadratning A uchidan AE va AF to`g`ri chiziqlar ,C uchidan esa BD diagonalga parallel bo`lgan CF to`g`ri chiziq o`tkazilgan. Agar kavadratning yuzi 3 ga teng bo`lsa, AFE uchburchakning yuzini toping. (97–9–108)

120 . AB||CD. OA=5; OB=4; AC=1,5 BD–?
(96–3–98)

121. AB||CD. OA=5; OB=4; OD=9; OC–? (96–9–38)

122. AB||CD. OA=5; OB=6; AC=2; BD–?
(96–12–100)

123. AB||CD. OB=6; BD=2,4; AC=2; OA–?
(96–13–40)

124. Perimetri 1 bo`lgan A<sub>1</sub>B<sub>1</sub>C<sub>1</sub> uchburchak A<sub>2</sub>B<sub>2</sub>C<sub>2</sub> uchburchakning tomonlari o`rtasini, A₂B₂C₂ uchburchak A₃B₃C₃ uchburchakning tomonlari o`rtasini, A<sub>3</sub>B<sub>3</sub>C<sub>3</sub> uchburchak esa A<sub>4</sub>B<sub>4</sub>C<sub>4</sub> uchburchakning tomonlari o`rtasini tutashtirsa, A₄B₄C₄ uchburchakning perimetri qancha bo`ladi? (97–4–44)
A) 3 B) 5 C) 4 D) 6 E) 8
125. Uchburchakning tomonlarini o`rtalarini tutashtirib, perimetri 65 ga teng bo`lgan uchburchak hosil qilindi. Berilgan uchburchakning perimetrini toping. (98–7–45)
A)32,5 B)260 C)75 D)195 E)130
126. ∆ABC ning tomonlari ∆A₁B₁C₁ ning mos tomonlaridan 2 marta katta. ∆ABC ning yuzi ∆A₁B₁C₁ ning yuzidan necha marta katta?
(98–7–47)
A)12 B)6 C)2 D)4 E)6
127. A₁B₁C₁ va A₂B₂C₂ uchburchaklar o`xshash. ∆A<sub>2</sub>B<sub>2</sub>C<sub>2</sub> ning yuzi ∆A<sub>1</sub>B<sub>1</sub>C<sub>1</sub> ning yuzidan 9 marta katta. ∆A<sub>1</sub>B<sub>1</sub>C<sub>1</sub> ning 3 ga teng bo`lgan tomoniga mos bo`lgan ∆A₂B₂C₂ ning tomonini toping.
(98–12–47)
A) 9 B) 27 C) 12 D) 6 E) 18
128. Perimetrlari 24 va 36 bo`lgan ikki o`xshash uchburchakning birining yuzi ikkinchisinikidan 10 ga ortiq . Kichik uchburchakning yuzini toping.
(97–3–46)
A) 20 B) 16 C) 8 D) 12 E) 18
129. Ikkita o`xshash uchburchakning yuzlari 6 va 24, ulardan birining perimetri ikkinchisinikidan 6 ga ortiq. Katta uchburchakning perimetrini toping. (96–7–46)
A) 18 B) 12 C) 20 D) 8 E) 24
130. Ikkita o`xshash uchburchakning perimetrlari 18 va 36, yuzlarining yig`indisi 30 ga teng. Katta uchburchakning yuzini toping. (97–7–46)
A) 20 B) 24 C) 21 D) 18 E) 25
131. ∆ABC ning tomonlari MN||AC to`g`ri chiziq bilan kesildi. ABC va MBN uchburchakning perimetrlari 3:1 kabi nisbatda. ABC uchburchakning yuzi 144 ga teng. MBN uchburchakning yuzini toping.
(97–2–39)
A) 16 B) 48 C) 32 D) 64 E) 56

132. ∆ABC ning AB tomoni MN||AC to`g`ri chiziq yordamida BM=2 va AM=4 bo`lgan klesmalarga ajratildi. Agar ∆MBN ning yuzi 16 ga teng bo`lsa, ∆ABC ning yuzi qanchaga teng bo`ladi?

(98–10–25)
A) 48 B) 96 C) 80 D) 144 E) 128
133. Yuzlari 8 va 32 bo`lgan ikkita o`xshash uchburchak perimetrlarining yig`indisi 48 ga teng. Kichik uchburchakning perimetrini toping.
(97–10–40)
A)12 B)16 C)20 D) 9,6 E)aniqlab bo`lmaydi
134. Uchburchakning asosiga parallel to`g`ri chiziq uning yuzini teng ikkiga bo`lsa, asosidan boshlab hisoblaganda, uning yon tomonlarini qanday nisbatda bo`ladi? (98–12–102)
A) ( –1):1 B) 1:1 C) :1
D) ( –1):1 E) (2 –1):1
135. Uchburchakning asosi 22 ga, yon tomonlari 13 va 19 ga teng. Asosiga tushirilgan medianasini toping. (98–1–42)
A) 18 B) 12 C) 16 D) 13 E) 14
136. Uchburchakning tomonlari 11 va 23 ga, uchinchi tomoniga tushirilgan medianasi 10 ga teng. Uchburchakning uchinchi tomonining toping.
(98–8–42)
A) 30 B) 15 C) 25 D) 28 E) 26
137. Tomonlari 10; 8 va 6 bo`lgan uchburchakning katta tomonga o`tkazilgan medianasini toping. (96–6–30)
A) 7 B) 6 C) 3 D) 4 E) 5

138. ABC uchburchakda AD mediana AB va AC tomonlar bilan mos ravishda 30⁰ va 60⁰ li burchak hosil qiladi. Agar AB= bo`lsa, AC ni toping.

(97–4–47)

139. CD– bissektrisa, AC=5, CB=7, AD=3. DB=?.
(97–4–47)

140. CD– bissektrisa, AC=6, CB=7, AB=8. AD=?.
(98–3–35)

141. AC=5, BC=10, BD=8, CD=? (00–10–69)

142. ABC uchburchakning B burchagi – to`g`ri burchak; N nuqta esa A va C burchaklar bissektrissalarining kesishish nuqtasi. ANC burchakning qiymatini toping. (99–4–38)
A)120⁰ B)150⁰ C)110⁰ D)135⁰ E)145⁰
143. Uchburchakning ikki tomonining nisbati 2:3 kabi. Uchinchi tomonining uzunligi 40 ga teng. Uchiinchi tomon qarshisidagi burchak bissektrissasi shu tomondan ajratgan katta qismining uzunligini toping. (00–2–35).
A) 25 B) 22 C) 26 D) 28 E) 24
144. Uchburchakning tomonlari 6;9 va 12 ga teng. Eng katta burchak bissektrisasi uchburchakning tomonidan ajratgan kesmalarning katta qismini uzunligini toping. (99–8–43).
A) 7,2 B) 4,8 C) 6,8 D) 8,4 E) 5,6
145. Perimetri 30 bo`lgan uchburchakning bissektrisasi uni perimetrlari 16 va 24 bo`lgan uchburchaklarga ajratadi. Berilgan uchburchakning bissektrisasini toping. (97–3–37).
A) 6 B) 8 C) 10 D) 7 E) 5
146. Piremetri 24 bo`lgan uchburchakning balandligi uni piremetrlari 14 va 18 bo`lgan ikkita uchburchakka ajratadi. Berilgan uchburchakning balanadligini toping. (96–7–37)
A) 10 B) 8 C) 6 D) 4 E) 3
147. Uchburchakning asosiga tushirilgan medianasi uni perimetrlari 18 va 24 ga teng ikkita uchburchakka ajratadi. Berilgan uchburchakning kichik yon tomoni 6 ga teng. Uning katta yon tomonini toping. (97–7–37)
A) 10 B) 12 C) 14 D) 9 E) 15
148. Uchburchakning 5 ga teng bo`lgan balandligi uni perimetrlari 18 va 26 ga teng ikkita uchburchakka ajratadi. Berilgan uchburchakning perimetrini toping. (97–10–37)
A) 29 B) 31 C) 34 D) 36 E) 39
149. ABC uchburchakda AC=6, DB=3 va DE=2 (AC||DE). AB tomonning uzunligini toping.
(99–7–35).

150. ∆ABC ning AB va BC tomonlari orasidagi burchak 30­⁰ ga teng. Agar AB va BC tomonlar orasidagi burchak 120­⁰ ga orttirilsa, ∆ABC ning yuzi qanday o`zgaradi? (98–10–22).
A) 4 marta ortadi B) 4 marta kamayadi
C) o`zgarmaydi D) marta ortadi
E) marta kamayadi
151. Agara uchburchakning asosi 20% ga uzaytirilib, balandligi 20% qisqartirilsa, uning yuzi qanday o`zgaradi? (97–4–55).
A) o`zgarmaydi B) 4% kamayadi
C) 4% ortadi D) 6% kamayadi
E) 6% ortadi.
152. Quyidagi mulohazalardan qaysi biri to`g`ri?
(96–6–15).
A) ihtiyoriy uchburchakning bissektrissalari kesishish nuqtasida 1:2 nisbatda bo`linadi.
B) ikkitadan tomoni va bittadan burchagi o`zaro teng bo`lgan uchburchaklar tengdir.
C) o`tmas burchakli uchburchakning o`tkir burchagi uchidan tushirilgan perpendikulyar uchburchakning ichida yotadi.
D) asosi va uchidagi burchagi teng bo`lgan teng yonli uchburchaklar tengdir.
E) qo`shni burchaklarning yig`indisi 180⁰ dan katta.
153. Quyidagi mulohazalardan qaysi biri to`g`ri?
(97–2–15).
A) Teng tomonli uchburchakning balandliklari kesishish nuqtasida 4:3 nisbatda bo`linadi.
B) ikkita to`g`ri burchakli uchburchakning gipotenuzalari va bittadan o`tkir burchaklari bir-biriga teng bo`lsa, bunday uchburchaklar tengdir.
C) Ikkita parallel to`g`ri chiziqni uchinchi to`g`ri chiziq bilan kesganda hosil bo`lgan ichki bir tomonlama burchaklar yig`indisi 180<sup>0</sup> dan kichik.
D) ikkitadan tomoni, bittadan burchagi o`zaro teng bo`lgan uchburchaklar tengdir.
E) teng yonli uchburchakning balandliklari hamda medianalari bir nuqtada kesishadi.
154. Quyidagi mulohazalardan qaysi biri noto`g`ri?
(97–8–15).
A) Teng tomonli uchburchakning balandliklari kesishish nuqtasida 2:1 nisbatda bo`linadi.
B) agar ikkita teng yonli uchburchakning asoslari va asoslaridagi burchaklari teng bo`lsa, bunday uchburchaklar tengdir.
C) qavariq besh burchakning ichki burchaklari yig`indisi 540<sup>0</sup> ga teng.
D) ikkita qo`shni burchakning yig`idisi 180<sup>0</sup> ga teng.
E) agar bir uchburchakning bir tomoni va shu tomon qarshisidagi burchagi, ikkinchi uchburchakning bir tomoni va shu tomon qarshisidagi burchagiga mos ravishda teng bo`lsa, bu uchburchaklar tengdir.
155. Quyidagi mulohazalardan qaysi biri noto`g`ri?
(97–12–44).
A) Agar ikkita teng tomonli uchburchaklarning balandliklari teng bo`lsa, bu uchburchaklar tengdir.
B) Agar ikki to`g`ri chiziqni uchinchi to`g`ri chiziq kesib o`tganda bir tomondagi tashqi burchaklar yig`indisi 180<sup>0</sup> ga teng bo`lsa, bu ikki to`g`ri chiziq paralleldir.
C) To`g`ri chiziqdan tashqarida yotgan nuqatadan bu to`g`ri chiziqqa faqat bitta perpendikulyar to`g`ri chiziq o`tkazish mumkin.
D) Uchburchakning barcha tashqi burchaklari yig`indisi 180⁰ ga teng.
E) agar bir uchburchakning uch tomoni ikkinchi uchburchakning uch tomoniga mos ravishda teng bo`lsa, bu uchburchaklar tengdir.
156. Uchburchakning tomonlari a, b va c ga teng. Bu uchburchakning tomonlari orasida munosbat o`rinli bo`lsa, uzunligi a ga teng tomon qarshisidagi burchakni toping.
(96–6–40).
A) 60⁰ B) 150⁰ C) 120⁰ D)90⁰ E)135⁰
157. Uchburchakning tomonlari a, b va c tomonlari orasida munosbat o`rinli bo`lsa, uzunligi a ga teng tomon qarshisidagi burchakni toping. (98–10–27).
A) 60⁰ B) 120⁰ C) 30⁰ D) 150⁰ E) 45⁰
158. Uchburchakning tomonlari m, n va k. tenglikni qanoatlantiradi. Uzunligi m ga teng tomon qarshisidagi burchakni toping. (97–2–40).
A) 45⁰ B) 150⁰ C) 120⁰ D)90⁰ E)135⁰
159. Uchburchakning b va c ga teng tomonlari orasidagi burchagi 30⁰ ga teng. Uchburchakning uchinchi tomoni 12 ga teng bo`lsa, hamda uning tomonlari shartni qanoatlantirsa, c ning qiymatini toping. (98–9–50).

160. Uchburchakning tomonlari a, b va c tomonlari orasida munosbat o`rinli bo`lsa, uzunligi a ga teng tomon qarshisidagi burchakni toping. (97–8–39).
A) 135⁰ B) 140⁰ C) 125⁰ D) 150⁰ E) 120⁰
161. Uchburchakning tomonlari a, b va c tomonlari orasida munosbat o`rinli bo`lsa, uzunligi a ga teng tomon qarshisidagi burchakni toping. (97–12–39).
A) 60⁰ B) 45⁰ C) 150⁰ D) 135⁰ E) 30⁰
162. Agar m>n>0 bo`lib, va uchburchakning tomonlarining uzunliklari bo`lsa, quyidagi tasdiqlardan qaysi biri to`g`ri?
(00–1–55).
A) Uchburchak o`tkir burchakli
B) Uchburchak o`tkir burchakli
C) Uchburchak to`g`ri burchakli
D) asosidagi burchaklari 45⁰ ga teng bo`lmagan teng yonli uchburchak
E) muntazam uchburchak
163. ABC uchburchak AB=3, CB=4 va bo`lsa, AC ning qiymatini toping. (99–7–33).
A) 2 B) 4 C) 3 D) 6 E) 1
164. (96–13–36).

165 uchburchakning tomonlari 3;5 va 6 ga teng. 5 ga teng bo`lgan tomon qarshisidagi burchakning kosinusini toping. (98–5–33).

166. ABC uchburchakda A=60⁰ va AB>BC bo`lsa, B ning mumkin bo`lgan x qiymatlari qaysi javobda to`g`ri ko`rsatilgan? (00–2–39).
A) 0⁰0 B) 30⁰0 C) 0⁰0
D) 60⁰0 E) 60⁰0
167. ABC uchburchakning AB, BC va CA tomonlarida olingan M, N va P nuqtalar shu tomonlarni 1:2 nisbatda bo`ladi. Agar ABC uchburchakning yuzi S ga teng bo`lsa, MNP uchburchakning yuzini toping. (00–3–76).

168. ABC uchburchakning AD medianasi 6 ga, AC tomoni 8 ga va ular orasidagi burchak 30⁰ ga teng. ABC uchburchakning yuzini toping. (99–10–47).
A) 28 B) 26 C) 22 D) 30 E) 24
169. ABC uchburchakda AB=AC, BM AC, BM=9 va MA=12. ∆ABC uchburchakning yuzini toping. (00–1–53).
A) 63,5 B) 64,5 C) 65,5 D) 67,5 E) 66,5
170. ABC uchburchakning AB va AC tomonlarida shunday K va N nuqtalar olindiki, ga va ga teng bo`ldi. ABC uchburchakning yuzi 18 ga teng. AKN uchburchakning yuzini toping. (99–3–46).
A) 4 B) 6 C) 9 D) 2 E) 3
171.Uchburchakning ikki tomoni uzunliklari 6 va 3 ga teng. Agar bu tomonlarga o`tkazilgan balandliklar uzunliklari yig`indisining yarmi uchinchi tomonga o`tkazilgan balandlikka teng bo`lsa, uchinchi tomon uzunligini aniqlang.
(99–8–45).
A) 6 B) 5 C) 3 D) 4 E) 7
172. Teng yonli uchburchakning asosi a ga, uchidagi burchagi α ga teng. Uchburchakning yon tomoniga tushirilgan balandligini toping. (97–11–34).

173. Teng yonli uchburchakning uchidagi burchagi β ga, yon tomoniga tushirilgan balandligi h ga teng. Uchburchakning asosini toping. (97–1–34).

174. Teng yonli uchburchakning uchidagi burchagi β ga, asosiga tushirilgan balandligi m ga teng. Uchburchakning yon tomoniga tushirilgan balandlikni aniqlang. (97–6–34).

175. Uchburchakning ikkita burchagi yig`indisining kosinusi ga teng. Uchinchi burchagining kosinusini toping. (96–3–55).

176. Uchburchakning ikkita burchagi yig`indisining kotangensi ga teng. Uchinchi burchagining kotangensi toping. (97–9–106).

177. Uchburchakning ikkita burchagi yig`indisining sinusi ga teng. Uchinchi burchagining sinusini toping. (97–4–46).

178. Uchburchakning ikkita burchagi yig`indisining kosinusi ga teng. Uchinchi burchagining kosinusini toping. (96–11–57).