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Primary Geo

Posted: Mon Feb 27, 2012 2:05 pm
by sakibtanvir
Consider, $O$ is a point inside $\triangle ABC$.Prove that, $AB+AC>BO+CO$ .

Re: Primary Geo

Posted: Tue Feb 28, 2012 2:49 pm
by nafistiham
priamary geo.png
priamary geo.png (90.54 KiB) Viewed 2825 times
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,
\[AC+AD+BD+OD>CD+BO\]
\[\Rightarrow AC+AB+OD>BO+CO+OD\]
\[\Rightarrow AC+AB>BO+CO\]