3 -bob planimetriya 1 Burchaklar. Masofalar

10. (97-10-37) Uchburchakning 5 ga teng bo'lgan balandligi uni perometrlari 18 va 26 bo'lgan ikkita

uchburchakka ajratadi. Berilgan uchburchakning perimetrini toping.

A) 29 B) 31 C) 34 D) 36 E) 39

11. (98-7-45) Uchburchakning tomonlari o'rtalarini tutashtirib, perimetri 65 ga teng bo'lgan uch-

burchak hosil qilindi. Berilgan uchburchakning perimetrini toping.

A) 32, 5 B) 260 C) 75 D) 195 E) 130

12. (00-8-66) Agar uchburchakning tomonlari turli butun sonlar bo'lib, uning perimetri 15 ga teng

bo'lsa, tomonlarini aniqlang.

A) 3; 5; 7 B) 4; 4; 7 C) 4; 5; 6 D) 3; 4; 8 E)3; 5; 7 yoki 4; 5; 6

13. (00-8-23) Teng yonli uchburchakning perimetri10 ga teng, yon tomoni asosidan 12 marta uzun.

Uchburchakning asosi qanchaga teng?

A) 0,4 B) 0,8 C) 0, 5 D) 0, 6 E ) 0,7

14. (01-2-42) ABC teng yonli uchburchakda AB = BC, AB-AC = 3dm, perimetri 18 dm. AB+AC

necha dm bo'ladi?

A) 15 B) 7 C) 13 D) 9 E) 11

15. (99-4-35) 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 tomonning uzunligini toping.

A) 6,5 B) 13 C) 5 D) 7 E)5

16. (97-7-64) Uchburchakning ikkita tomoni 0; 8 va 1,9 ga teng. Uchinchi tomonning uzunligi butun

son ekanligini bilgan holda shu tomonni toping.

A) 1 B) 2 C) 3 D) 4 E) bunday tomon mavjud emas

17. (97-9-57) Uchburchakning ikkita tomoni 0,5 va 7,9 ga teng. Uchinchi tomonning uzunligi butun

son ekanligini bilgan holda shu tomonini toping.

A) 8 B) 7 C) 6 D) 5 E) 4

18. (98-4-42) Uzunligi 1; 3; 5; 7; 9 ga teng bo'lgan kesma lar berilgan. Bu kesmalardan tomonlari har xil bo'lgan nechta turli uchburchak yasash mumkin?

A) 4 B) 3 C) 5 D) 2 E) 6

19. (00-5-54) Teng yonli ABC uchburchakda A va C burchaklar teng. AB : AC = 5 : 3 va AB-AC =3 ga teng. Uchburchakning perimetrini toping.

A) 19, 5 B) 18, 5 C) 17, 5 D) 16 E) 15

20. (03-5-25) Uchburchakning tomonlari 9; 15 va x ga teng. Uchburchakning yarim perimetri qaysi

oraliqqa tegishli bo'ladi?

A) (15; 24) B) (6; 28) C) (9; 15) D) 30; 48 E) (18; 30)

21. (03-6-75) Uchburchakning balandligi 4 ga teng. Bu balandlik uchburchakni perimetrlari mos rav-

ishda 16 va 23 ga teng bo'lgan ikkita uchbur chakka ajratadi. Berilgan uchburchakning peri-

metrini toping.

A) 31 B) 30 C) 28 D) 32 E) 34

22. (03-10-57) Tomonlari 20; 20 va 30 m bo'lgan uch burchak shaklidagi maydonning atrofini o'rash uchun

ustunlar o'rnatildi. Agar ustunlar orasidagi masofa 5 m dan bo'lsa, nechta ustun kerak bo'ladi?

A) 15 B) 14 C) 16 D) 13 E) 18

3.3.2 Uchburchak burchaklari.

1. Uchburchak burchaklarining yig'indisi 180⁰ ga teng. (99-6-3) Uchburchak burchaklarining kattaliklari 2; 3

va 10 sonlariga proporsional. Uchburchakning burchaklarini toping.

A) 24⁰; 36⁰; 120⁰ B) 20⁰; 46⁰; 120⁰ C) 10⁰; 50⁰; 120⁰ D) 30⁰; 40⁰; 110⁰ E) 60⁰; 90⁰; 10⁰

Yechish: Uchburchak burchaklari 2; 3 va 10 sonlar iga proporsional bo'lgani uchun bu burchaklarni 2x; 3x;

10x ko'rinishda yozish mumkin. Uchburchak ichki bur chaklar yig'indisi 1800 ga teng bo'lgani uchun 2x +3x + 10x = 1800 bo'ladi. Bu yerdan 15x = 180⁰ va x = 12⁰ ekani kelib chiqadi. Uchburchakning burchak-

lari 2x = 24⁰, 3x = 36⁰, 10x = 120⁰ ekan. J: (A).

1. (96-3-55) Uchburchak ikkita burchagi yig'indisining kosinusi ga teng. Uchinchi burchagining kosi-

nusini toping.

A) B) C) D) E)

2. (96-6-18) ABC uchburchakda A uchdagi tashqi burchagi 120⁰ ga, C uchidagi ichki burchak 80⁰

ga teng. B uchdagi tashqi burchakni toping.

A) 160⁰ B) 150⁰ C) 130⁰ D) 120⁰ E) 140⁰

3. (96-7-36) Uchburchakning ikkita burchagi qiymatlarining nisbati 1 : 2 kabi. Uchinchi burchagi shu

burchaklarning kichigidan 40⁰ ga katta. Uchburchakning katta burchagini toping.

A) 102 ⁰ B) 93⁰ C) 75⁰ D) 80⁰ E) 105⁰

4. (96-11-57) Uchburchak ikkita burchagi yig'indi sining kosinusi ga teng. Uchinchi burchagining

kosinusini toping.

A) B) C) D) E) ¡13

5. (96-12-35) Uchburchak ikkita burchagi yig'indisi-

ning kosinusi 1

2 ga teng. Uchinchi burchagining

kosinusini toping.

A) 2

3 B) 1

3 C) ¡1

2 D) 1

2 E) ¡1

3

6. (97-3-36) Uchburchak ikkita burchagining qiymat-

lari nisbati 3 : 4 kabi, uchinchisiniki esa shu bur-

chaklarning kattasidan 40 ga katta. Uchburchakn-

ing katta burchagini toping.

A) 840 B) 680 C) 960 D) 640 E) 720

7. (97-4-46) Uchburchak ikki burchagi yig'indisining sinusi 13 bo'lsa, uchinchi burchagining sinusi qanchaga teng bo'ladi?

A) B) C) D) E)

8. (97-5-43) Agar uchburchakning A, B va C burchaklari 1; 2 va 3 sonlariga proporsional bo'lsa, B

burchakni toping.

A) 30⁰ B) 60⁰ C) 90⁰ D) 45⁰ E) 120⁰

9. (97-7-36) Uchburchak ikkita burchagining qiymatlari nisbati 5 : 9 kabi, uchinchi burchagi shu bur-

chaklarning kichigidan 10⁰ ga kichik. Uchburchakning eng kichik burchagini toping.

A) 30⁰ B) 40⁰ C) 45⁰ D) 50⁰ E) 20⁰

10. (97-9-43) Agar uchburchakning burchaklari 5; 6 va 7 sonlariga proporsional bo'lsa, uchburchakn-

ing katta burchagini toping.

A) 75⁰ B) 80⁰ C) 50⁰ D) 40⁰ E) 70⁰

11. (97-9-106) Uchburchak ikki burchagi yig'indisining kotangensi bo'lsa, uchinchi burchagining kotan-

gensini toping.

A) B) C) D) E)

12. (97-10-36) Uchburchak ikkita burchagining kattaliklari nisbati 3 : 2 ga teng. Uchinchi burcha-

gi shu burchaklarning kattasidan 60⁰ ga kichik.Uchburchakning kichik burchagini toping

A) 50⁰ B) 45⁰ C) 40⁰ D) 30⁰ E) 15⁰

13. (98-2-45) Uchburchakning ikkita tashqi burchagi yig'indisi 240⁰ ga teng. Uning shu burchaklarga

qo'shni bo'lmagan ichki burchagini toping.

A) 30⁰ B) 45⁰ C) 90⁰ D) 75⁰ E) 60⁰

14. (99-4-38) ABC uchburchakning B burchagi to'g'ri burchak; N nuqta esa A va C burchaklar bissek-

trisalarining kesishish nuqtasi. ANC burchakning qiymatini toping.

A) 120⁰ B) 150⁰ C) 110⁰ D) 135⁰ E) 145⁰

15. (00-2-39) ABC uchburchakda 6 A = 600 va AB >BC bo'lsa, 6 B ning mumkin bo'lgan x qiymatlari

qaysi javobda ko'rsatilgan?

A) 0⁰ < x < 60⁰ B) 30⁰ < x < 60⁰ C) 0⁰ < x < 30⁰ D) 60⁰ < x < 120⁰ E) 60⁰ < x < 90⁰

16. (00-3-73) Uchburchakning 108⁰ li tashqi burchagiga qo'shni bo'lmagan ichki burchaklarining nis-

bati 5 : 4 kabi. Shu ichki burchaklarning kichigini toping.

A) 45⁰ B) 40⁰ C) 72⁰ D) 48⁰ E) 30⁰

17. (00-6-34) Uchburchakning ikkita tashqi burchaklari 120⁰ va 160⁰ ga teng. Uning uchinchi tashqi

burchagini toping.

A) 100⁰ B) 80⁰ C) 90⁰ D) 70⁰ E) 60⁰

18. (00-8-62) Agar A, B va C lar uchburchakning burchaklari bo'lsa, sin A+B2 nimaga teng?

A)sin B)cos C) - sin D) sinC E) cosC

19. (97-1-28) Teng yonli uchburchakning yon tomoniga tushirilgan balandligi bilan ikkinchi yon tomon

orasidagi burchak 20⁰ ga teng. Teng yonli uchburchakning asosidagi burchagini toping.

A) 50⁰ B) 48⁰ C) 55⁰ D) 58⁰ E) 65⁰

20. (97-2-18) Teng yonli uchburchakning uchidagi tashqi burchagi o'sha uchdagi ichki burchagidan 4 mar-

ta katta. Uchburchakning asosidagi tashqi burchagi necha gradus?

A) 100⁰ B) 102⁰ C) 96⁰ D) 108⁰ E) 104⁰

21. (97-6-28) Teng yonli uchburchakning uchidagi burchagi 94⁰. Asosidagi burchaklarining bissektrisalari

kesishishidan hosil bo'lgan o'tkir burchakni toping.

A) 37⁰ B) 43⁰ C)48⁰ D) 47⁰ E) aniqlab bo'lmaydi

22. (97-8-18) Teng yonli uchburchakning uchidagi burchagi 80⁰ ga teng. Yon tomoniga o'tkazilgan balandlik va asosi orasidagi burchakni toping.

A) 35⁰ B) 45⁰ C) 30⁰ D) 40⁰ E) 50⁰

23. (98-11-81) Teng yonli uchburchakning asosidagi burchagi 400 ga teng. Bu uchburchakning yon tomonlari orasidagi burchakka qo'shni bo'lgan tashqi burchagining qiymatini toping.

A) 90⁰ B) 100⁰ C) 140⁰ D) 50⁰ E) 80⁰

24. (99-4-37) Teng yonli uchburchakning uchidagi burchagi 30⁰ga teng. Uning yon tomoniga tushirilgan balandligi bilan asosi orasidagi burchakni toping.

A) 75⁰ B) 15⁰ C) 20⁰ D) 45⁰ E) 65⁰

25. (00-6-36) Teng yonli uchburchakning asosidagi burchagi 30⁰ ga teng. Shu uchburchakning yon tomoni

va ikkinchi yon tomoniga tushirilgan balandligi orasidagi burchakni toping.

A) 75⁰ B) 60⁰ C) 45⁰ D) 40⁰ E) 30⁰

26. (00-6-37) Teng yonli ABC uchburchakda AC-asos, CD - C burchakning bissektrisasi va 6 ADC =1500 ga teng bo'lsa, burchak B ning kattaligini toping.