Tavi - Ganatleba

3 A
moc: ∆ABC;
m ; m ; a.
a b
O
B
D
C
K
u.v. S ∆ABC .
I Tavi
2
BOD samkuTxedis samive gverdi wiTelia. BO= mb ,
3
OD= 3
1 1
ma , BD= a. heronis formuliT vpoulobT S∆BOD ,
2
S ∆ABC =6·S ∆BOD .
4 C
moc: ∆ABC;
m ; m ; c.
a b
O
A B
5
B
N M
O
A С
K
D
savarjiSoebi
1
2
3
u.v. S ∆ABC .
∆AOB-Si samive gverdi wiTelia. A
2
AO= ma , BO=
3 3
lobT S ∆AOB , S ∆ABC = ·S ∆AOB .
moc: ∆ABC;
m a ; m b ; c.
u.v. S ∆ABC .
2 mb , AB=c. heronis formuliT vpou-
OK-s gagrZelebaze gadavdoT KD=OK monakveTi.
Teorema 1-is I Sedegis Tanaxmad S =S ≡S,
∆OKC ∆CKD
∆AOK=∆KDC (ori gverdiT da maT Soris mdebare
2 ma .
kuTxiT), e.i. DC=AO=
3
2 2
∆ODC-Si viciT sami gverdi. DC= ma ; OC= mc ; OD=
3 3 3
heronis formuliT vpoulobT S ∆ODC , S ∆ABC = ·S ∆ADC .
2 mb .
ABC samkuTxedSi gavlebulia medianebi AA , BB da CC . O maTi
1 1 1
gadakveTis wertilia. A A-dan CC -ze daSvebulia A N perpendikulari.
1 1 1
1
ipoveT fardoba CA :AO, Tu S = 1 ∆OA1N 12 S∆ABC .
tolferda samkuTxedis medianebia 15, 15 da 18. ipoveT samkuTxedis
farTobi.
ipoveT samkuTxedis farTobi, Tu misi ori gverdi Sesabamisad udris
7sm-s da 9sm-s, mesame gverdis mediana ki udris 6sm-s.
19