Tavi - Ganatleba

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I Tavi 0 4 5* 6 ipoveT farTobi samkuTxedisa, romlis medianebi urTierTperpendikularulia da 5-isa da 9-is tolia. ipoveT ABC samkuTxedis AC gverdze daSvebuli simaRle, Tu AC=a da S ∆AOC =Q, sadac O medianebis gadakveTis wertilia. S farTobis mqone tolferda samkuTxedSi ferdebis medianebis mier Seqmnili im kuTxis sidide, romelic fuZis mopirdapired mdebareobs, a-s tolia. ipoveT am samkuTxedis fuZis sigrZe, Tu S=900, sin � 3 = 2 5 .
I Tavis mokle mimoxilva B A C B cx ax A C B cx ax A C bx samkuTxedebis msgavsebis niSnebi B 1 A 1 C 1 B 1 c a A 1 C 1 B 1 c a A C 1 1 b I Tavi 1 Tu erTi samkuTxedis ori kuTxe meore samkuTxedis ori kuTxis tolia, maSin es samkuTxedebi msgavsia. ∠A=∠A 1 , ∠B=∠B 1 , maSin ∆ABC~∆A 1 B 1 C 1 . 2 Tu erTi samkuTxedis ori gverdi meore samkuTxedis ori gverdis proporciulia da am gverdebiT Seqmnili kuTxeebi tolia, maSin es samkuTxedebi msgavsia. AB BC = , ∠B=∠B , maSin ∆ABC~∆A B C . A1B1 B1C 1 1 1 1 1 3 Tu erTi samkuTxedis gverdebi meore samkuTxedis gverdebis proporciulia, maSin es samkuTxedebi msgavsia. AB BC AC = = , A1B1 B1C1 A1C1 maSin ∆ABC~∆A 1 B 1 C 1 . Tu ∆ABC~∆A 1 B 1 C 1 , maSin a b c ma la ha r R P = = = = = = = = = a1 b1 c1 m l h r1 R1 P a1 a1 a1 1 , √S √ sadac m a , l a , h a -iT aRiniSneba Sesabamisad a gverdis mediana, biseqtrisa da simaRle. r da R ki Caxazuli da Semoxazuli wrewiris radiusebia, P perimetria. S 1 1
Page 2 and 3: I Tavi §1 samkuTxedebis msgavsebis
Page 4 and 5: 4 I Tavi sf g savarjiSoebi 1 2 3 4
Page 6 and 7: 6 I Tavi g amocana 1 ABC samkuTxedi
Page 8 and 9: 8 I Tavi g g amocana 1 mocemulia
Page 10 and 11: I Tavi 10 §5 proporciuli monakveTe
Page 12 and 13: 1 I Tavi 3* 4 5 6 7 8 9 10 11 12* 1
Page 14 and 15: I Tavi 14 amocana 1 A amocana 2 A O
Page 16 and 17: I Tavi 16 §7 heronis formula B a A
Page 18 and 19: I Tavi 18 1 Tema §8 rogor gamovTva
Page 22 and 23: I Tavi C C A O C B D M O O B B N a
Page 24 and 25: I Tavi 4 g 12 13 14 15 16 17 18 19
Page 26 and 27: I Tavi 6 7 8 9 10 11 A D D 6 sm 5x
Page 28: I Tavi 8 8 9 10 11 erTi wertilidan

Tavi - Ganatleba

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