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# Inequality

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If D is a point inside triangle ABC, then prove that AB + AC \(\ge\) DB + DC

I know this seems intuitive, but I don't know how to prove it.

Jul 18, 2019

#1
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Let D be any point in the interior of ABC.....draw BD  and extend this to E, lying on AC

So.....

DE + EC > DC      ....  add BD to both sides

(DE + BD) + EC > DC + BD

BE + EC > DC + BD

AB + AE > BE .......add EC to both sides

AB + (AE + EC) > BE + EC

AB + AC > BE +EC           which implies that

AB + AC > DC + BD

Jul 18, 2019
edited by CPhill  Jul 18, 2019
#2
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Thanks

MaxWong  Jul 19, 2019