ko‘pburchaklar va aylana

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1629119524.doc n 0 180 2 1 n 0 360 n 0 180 n 0 180 n 0 180 в 2 1 3 h 3 2 h 0 30 cos h 3 2 h 3 2 h 3 4 h 3 3 a 3 3 a 12 a p 12 a p 2 1 2 2 n в вс - 2 2 nc аn + 2 2 1 авс s ас вс ав d × × 4 2 2 2 p 2 2 вс ав + 2 2 а ) 2 sin 2 ( 2 2 p p - r 8 ) 2 ( 2 - p а 8 ) 2 ( 2 - p а a r ав mn ав ве 2 = = a r q s a r = 2 p q s a r p 2 = q s p 4 2 1 n 0 180 n …

ar ichida faqat to‘g‘ri to‘rtburchakka tashqi aylana chizish mumkin. 2) trapetsiyalar ichida faqat teng yonli trapetsiyaga tashqi aylana chizish mumkin. esda tutish foydali: 1. ptolomey teoremasi: ichki chizilgan to‘rtburchakda diagonallar ko‘paytmasi uning qarama-qarshi tomonlari ko‘paytmalari yig‘indisiga teng. 2. ichki aylana chizish mumkin bo‘lgan teng yonli trapetsiya balandligi, uning asoslarini o‘rta geometrigi bo‘ladi: h2 =a ∙ 1- misol. agar teng yonli trapetsiyani katta asosi a, kichik asosi bilan yon tomoni 1200 burchak hosil qilsa, unga ichki chizilgan doira yuzini toping. yechish: dk = h desak, h= 2 r bo‘ladi, bu yerda r – ichki chizilgan doira radiusi. adk uchburchakdan ak = h ∙ tg300 = ni topamiz. dc= ab – 2ak = a – ad = bc = = trapetsiyaga aylana ichki chizilganligidan ab+dc = ad+bc, h ni aniqlash tenglamasini hosil qilamiz: 2a – = demak, h = , u holda r = . izlanayotgan yuza . javob: . 2 – …

bad = arcsin , q = 8, s = π bo‘lganda < bad = arcsin = 300 javob: 300 5 – misol. tomoni a ga teng muntazam oltiburchakka aylana ichki chizilgan va aylana tashqi chizilgan. bu aylanalar hosil qilgan halqa yuzasini toping. yechish: tashqi chizilgan aylana radiusi r ni an = 2rsin formuladan topamiz n = 6 da r = a. u holda ichki chizilgan aylana radiusi r = rcos = bundan halqa yuzi π (r2 – r2 ) = ekanligini ko‘rish mumkin. javob: 6 – misol. teng yonli trapetsiyaning balandligi h, yon tomoni tashqi chizilgan aylana markazidan α burchak ostida ko‘rinadi. trapetsiyani yuzini toping. yechish: chizmadan ko‘rinadiki, burchak ichki chizilgan burchak ekanligidan bc yoyni yarmi bilan o‘lchanadi, demak, = ab = ak+kb, dc =ak – ae = ak – kb, ak = h · ctg , bularga ko‘ra izlanayotgan yuza: s = (ab +dc)· h = ak · h …

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1629119524.doc n 0 180 2 1 n 0 360 n 0 180 n 0 180 n 0 180 в 2 1 3 h 3 2 h 0 30 cos h 3 2 h 3 2 h 3 4 h 3 3 a 3 3 a 12 a p 12 a p 2 1 2 2 n в вс - 2 2 nc аn + 2 2 1 авс s ас вс ав d × × 4 2 2 2 p 2 2 вс ав + 2 2 а ) 2 sin 2 ( 2 2 p p - r 8 ) 2 ( 2 - p а 8 ) 2 ( 2 - p а a r ав mn ав …

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