Hauv qhov kev tshaj tawm no, peb yuav xav txog ib qho ntawm cov ntsiab lus tseem ceeb ntawm Euclidean geometry - Stewart's theorem, uas tau txais lub npe zoo li no hauv kev hwm ntawm Askiv lej M. Stewart, uas tau ua pov thawj nws. Peb kuj tseem yuav tshuaj xyuas kom meej ib qho piv txwv ntawm kev daws qhov teeb meem los sib sau ua ke cov ntaub ntawv nthuav tawm.
Nqe lus ntawm lub theorem
Dan daim duab peb sab ABC. Los ntawm nws sab AC taw tes noj D, uas txuas nrog rau sab saum toj B. Peb lees txais cov lus hauv qab no:
- AB = a
- BC = IB
- AB = p
- AD = x
- DC = thiab
Rau daim duab peb sab no, qhov sib npaug yog qhov tseeb:
Kev siv theorem
Los ntawm Stewart's theorem, cov qauv tuaj yeem muab tau los nrhiav qhov nruab nrab thiab bisectors ntawm daim duab peb sab:
1. Qhov ntev ntawm lub bisector
cia lc yog lub bisector kos rau sab c, uas muab faib ua ntu x и y. Cia peb coj ob sab ntawm daim duab peb sab li a и b… Hauv qhov no:
2. Qhov nruab nrab ntev
cia mc yog qhov nruab nrab tig mus rau sab c. Cia peb qhia txog ob sab ntawm daim duab peb sab li a и b… Tom qab ntawd:
Piv txwv ntawm qhov teeb meem
Daim duab peb sab muab ABC. Nyob rau sab AC sib npaug li 9 cm, taw tes noj D, uas faib rau sab li ntawd AD ntev dua ob zaug DC. Qhov ntev ntawm ntu txuas lub vertex B thiab taw tes D,,5 cm. Nyob rau hauv cov ntaub ntawv no, tsim daim duab peb sab US yog isosceles. Nrhiav qhov seem ntawm daim duab peb sab ABC.
tshuaj
Cia peb piav qhia txog cov xwm txheej ntawm qhov teeb meem hauv daim duab kos duab.
AC = AD + DC Luas = 9 cm. AD ntev DC ob ob,ie AD = 2DC.
Thiaj li, lub 2DC + DC = 3DC u9dXNUMXcm ua. Yog li ntawd, DC luas = 3 cm, AD Luas = 6 cm.
Vim daim duab peb sab US - isosceles, thiab sab AD yog 6 cm, ces lawv sib npaug AB и BDIe AB Luas = 5 cm.
Nws tsuas yog nrhiav tau xwb BC, muab cov qauv los ntawm Stewart's theorem:
Peb hloov cov txiaj ntsig paub rau hauv qhov kev qhia no:
Txoj kev no, BC = √52 7,21 cm.