Tavi - Ganatleba
Tavi - Ganatleba
Tavi - Ganatleba
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I <strong>Tavi</strong><br />
14<br />
amocana 1<br />
A<br />
amocana 2<br />
A<br />
O<br />
D<br />
B<br />
savarjiSoebi<br />
1<br />
2<br />
O<br />
D<br />
M<br />
C<br />
C<br />
M<br />
B<br />
ACA da CB monakveTebi wrewirs kveTs Sesabamisad D da<br />
M wertilebSi. daamtkiceT, rom ΔDCM~ΔBCA.<br />
damtkiceba:<br />
C wertilidan gavlebulia ori mkveTi – CA da CB,<br />
maSasadame,<br />
CD CB<br />
CD·CA=CM·CB ⇒ = . DCM da BCA.<br />
CM CA<br />
samkuTxedebisaTvis C kuTxe saerToa, msgavsebis niSnis<br />
Tanaxmad, ΔDCM~ΔBCA. r.d.g.<br />
monakveTi wrewiris diametria. CA da CB mkveTebi<br />
wrewirs kveTs Sesabamisad D da M wertilebSi.<br />
ipoveT ∠CBD, Tu S ∆DCM :S ∆ACB =1:4.<br />
amoxsna:<br />
∠ADB=90°, rogorc diametrze dayrdnobili Caxazuli<br />
kuTxe. zemoT ganxiluli amocanis Tanaxmad,<br />
DC √S�DCM<br />
1<br />
ΔDCM~ΔBCA ⇒ = = .<br />
BC √S<br />
2<br />
�ABC<br />
ganvixiloT ΔCBD; ∠D=90°.<br />
DC 1<br />
1<br />
= ⇒ sin∠CBD=<br />
BC 2 2<br />
pasuxi: ∠CBD= 0°.<br />
⇒ ∠CBD= 0°.<br />
samkuTxedis perimetria 10 sm, misi farTobi ki – sm . ipoveT mocemuli<br />
samkuTxedis msgavsi samkuTxedis perimetri, Tu misi farTobia 1 sm .<br />
ABC samkuTxedSi AB<br />
gverdze aRebuli M wertilidan gavlebulia AC gverdis<br />
paraleluri MN monakveTi. ipoveT MN-is sigrZe, Tu S =18sm ΔABC 2 ,<br />
S =4sm da AC= sm.<br />
ΔMNB
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