Aylana va doira

Javob: ( )
5

– misol. O markazli har xil radiusli ikkita doira berilgan. Kichik doiraga o`tkazilgan urinmani katta doira bilan hosil qilgan kesmasi 32 sm. Agar halqani eni 8 sm bo`lsa katta doira radiusini toping.
Yechish:
Shartga ko`ra AB = 32 sm, CD=8sm,
Shuningdek OC  AB. Katta doira radiusi-
ni R desak, u holda OCB to`g`ri burchakli
uchburchakdan:


OB² = OC² + CB² yoki R²= (R – 8)² + 16² , R = 20 sm.

Javob: 20 sm
6 – misol. Umumiy vatarga tiralgan ikki doirani mos yoylari 60⁰ va 120⁰. Doiralar yuzalari nisbatini toping.
Y

echish:
O₁B = r, O₂B = R deb belgilaymiz.
Shartga ko`ra < A O<sub>1</sub>B = 120<sup>0</sup> , <sub>2</sub>B = 60<sup>0</sup>.
Ikki aylana markazlari orasidagi O<sub>1</sub>O<sub>2</sub>
kesma AB ga perpendikulyar, u holda
,
bundan R = 2BC, demak
= R<sup>2</sup> : r<sup>2</sup> = 3 : 1 Javob:_3:1__7-_misol.'>Javob: 3:1
7- misol. Yoyi 120<sup>0</sup> , perimetri R bo`lgan segment yuzasini toping.
Yechish:
R doira radiusi. Bundan ACB yoyni aniqlaymiz:


= · 120⁰= πR .
AOB uchburchakdan AB = 2 R sin 60⁰ = R
Shartga ko`ra AB+ =R, demak
R + R =R, bundan R= .
S segmentni yuzi sektorni yuzidan
OAB uchburchak yuzini ayirishdan hosil bo`lgan son bo`ladi.
Shuning uchun
S = πR² – .
Javob:


8 – misol. Radiuslari R va r bo`lgan ikki aylana tashqi o`rinadi. Nuqtalari orasidagi kesmasini toping.