Planimetriya

Question 1

$ABC$ teng yonli ($AB=BC$) uchburchakning $BD$ medianasi uzunligi 4 cm ga teng. Agar $ABD$ uchburchak perimetri 12 cm ga teng bo‘lsa, $ABC$ uchburchak perimetrini (cm) toping.

Accepted Answer

16

Answer

9

Answer

8

Answer

18

Question 2

Ikki to‘g‘ri chiziqning kesishishidan hosil bo‘lgan qo‘shni burchaklarning ayirmasi $20^\circ$ ga teng bo‘lsa, bu burchaklardan kichigini toping.

Accepted Answer

$80^\circ$

Answer

$90^\circ$

Answer

$60^\circ$

Answer

$70^\circ$

Question 3

Rasmda berilgan ma’lumotlarga ko‘ra $x$ necha gradus?

Accepted Answer

$97^\circ$

Answer

$93^\circ$

Answer

$102^\circ$

Answer

aniqlab bo‘lmaydi

Question 4

Muntazam sakkizburchakka ichki va tashqi aylanalar chizilgan. Agar ichki chizilgan aylananing radiusi $r=2+\sqrt2$ cm bo‘lsa, bu aylanalar hosil qilgan halqaning yuzini (cm$^2$) toping.

Accepted Answer

$2\pi$

Answer

$4\pi$

Answer

$8\pi$

Answer

$\sqrt2\pi$

Question 5

Uchburchak tomonlari 41; 41; 80 ga teng bo‘lsin. Bissektrisalar kesishish nuqtasidan katta tomongacha bo‘lgan eng qisqa masofani toping.

Accepted Answer

$4\frac{4}{9}$

Answer

$4\frac{5}{9}$

Answer

3

Answer

4

Question 6

Rasmda berilgan ma’lumotlardan foydalanib, aylana uzunligini toping.

Accepted Answer

$10\pi$

Answer

$12\pi$

Answer

$9\pi$

Answer

$11{,}2\pi$

Question 7

Chizmadagi $ABCD$ parallelogrammning yuzi 64 cm$^2$ ga teng bo‘lsa, $FKCD$ to‘rtburchakning yuzini (cm$^2$) toping. Bunda $\frac{AF}{FD}=3$, $\frac{AK}{KB}=1$ ga teng.

Accepted Answer

36

Answer

52

Answer

48

Answer

28

Question 8

$ABCD$ rombda $AC>BD$ va $\frac{AC}{BD}-\frac{BD}{AC}=2$ bo‘lsa, $\angle A$ burchakni toping.

Accepted Answer

$45^\circ$

Answer

$30^\circ$

Answer

$\mathrm{arctg}\,2$

Answer

$2\,\mathrm{arctg}\,2$

Question 9

Aylana $13:14:9$ nisbatda uchta yoyga bo‘lingan va bo‘linish nuqtalari tutashtirilib uchburchak hosil qilingan. Agar hosil bo‘lgan uchburchakning kichik tomoni $\sqrt[4]{12}$ cm ga teng bo‘lsa, aylanaga tashqi chizilgan muntazam uchburchakning yuzini (cm$^2$) toping.

Accepted Answer

9

Answer

$2\sqrt[4]{3}$

Answer

36

Answer

$3\sqrt3$

Question 10

Chizmada $ABC$ to‘g‘ri burchakli uchburchak berilgan. Agar $AD\perp ED$, $\angle B=90^\circ$, $ED=6$, $S_{BEDC}=20$ va $S_{AED}=16$ bo‘lsa, $BC=x$ tomonning uzunligini toping.

Accepted Answer

9

Answer

12

Answer

10

Answer

8

Question 11

Teng yonli $ABCD$ trapetsiyaning yuzini toping.

Accepted Answer

28

Answer

11

Answer

24

Answer

21

Question 12

Rasmda teng yonli $ABCD$ trapetsiya tasvirlangan. Agar bu trapetsiyaning o‘rta chizig‘i 10 ga teng bo‘lsa, rasmda berilgan ma’lumotlardan foydalanib $DE$ kesma uzunligini toping.

Accepted Answer

6

Answer

8

Answer

7

Answer

5

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