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.

MaxWong Jul 18, 2019

#1**+6 **

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

CPhill Jul 18, 2019