Primary Geo

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sakibtanvir
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Primary Geo

Unread post by sakibtanvir » Mon Feb 27, 2012 2:05 pm

Consider, $O$ is a point inside $\triangle ABC$.Prove that, $AB+AC>BO+CO$ .
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nafistiham
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Re: Primary Geo

Unread post by nafistiham » Tue Feb 28, 2012 2:49 pm

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let us draw the ext. of $CO$, which intersects $AB$ at $D$
now, as we know summation of two sides of a triangle is greater than the third,
in $\triangle ACD$, $AC+AD>CD$
in $\triangle BOD$, $BD+OD>BO$
summing these two we can say,
\[AC+AD+BD+OD>CD+BO\]
\[\Rightarrow AC+AB+OD>BO+CO+OD\]
\[\Rightarrow AC+AB>BO+CO\]
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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