N'akwụkwọ a, anyị ga-atụle otu n'ime isi theorems nke Euclidean geometry - Stewart's theorem, nke natara aha dị otú ahụ iji sọpụrụ onye England mathematician M. Stewart, onye gosipụtara ya. Anyị ga-enyocha n'ụzọ zuru ezu ihe atụ nke idozi nsogbu ahụ iji mee ka ihe a na-egosiputa.
Nkwupụta nke theorem
Dan triangle ABC. N'akụkụ ya AC isi ihe were D, nke ejikọrọ na elu B. Anyị na-anabata nrịbama a:
- AB = a
- BC = b
- BD = p
- AD = x
- DC = na
Maka triangle a, nha anya bụ eziokwu:
Ngwa nke theorem
Site na usoro Stewart, enwere ike nweta usoro maka ịchọta medians na bisector nke triangle:
1. Ogologo nke bisector
ka lc bụ bisector na-adọta n'akụkụ c, nke kewara n'ime akụkụ x и y. Ka anyị were akụkụ abụọ nke ọzọ nke triangle dị ka a и b… N'okwu a:
2. Ogologo etiti
ka mc bụ etiti atụgharị gbadaa n'akụkụ c. Ka anyị gosi akụkụ abụọ ndị ọzọ nke triangle dị ka a и b… Mgbe ahụ:
Ọmụmaatụ nke nsogbu
Triangle nyere ABC N'akụkụ AC hà nhata 9 cm, isi ihe were D, nke na-ekewa akụkụ nke mere na AD okpukpu abụọ DC. Ogologo nke akụkụ na-ejikọta vertex B na isi D, bụ 5 cm. N'okwu a, triangle kpụrụ Abd bụ isosceles. Chọta akụkụ ndị fọdụrụ nke triangle ABC.
ngwọta
Ka anyị gosipụta ọnọdụ nke nsogbu ahụ n'ụdị eserese.
AC = AD + DC = 9 sentimita. AD aba DC ugboro abụọ, ya bụ AD = 2DC.
N'ihi ya, 2DC + DC = 3DC u9d XNUMX cm. Yabụ, DC = 3 cm, AD = 6 sentimita.
N'ihi na triangle Abd - isosceles, na akụkụ AD bụ 6 cm, ya mere ha hà nhata AB и BDIe AB = 5 sentimita.
Ọ na-anọgide naanị ịchọta BC, na-enweta usoro a site na Stewart's theorem:
Anyị na-eji dochie ụkpụrụ amaara n'ime okwu a:
N'ụzọ nke a, BC = √52 ≈ 7,21 cm.