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Prove EF + FG + GH + HE ≥ 2AC

Albert

Well-known member
Jan 25, 2013
1,225
Rectangle ABCD ,having fours points$ E,F,G,H $ located on segments AB, BC, CD,and

DA respectively , please prove :

$EF+FG+GH+HE\geq 2 AC $

and determine when the equivalence can be taken ?
 

Albert

Well-known member
Jan 25, 2013
1,225
Re: Ef+fg+gh+he>=2ac

suppose we have another three cards equivalent to figure 1 ,and rearranging these four cards
in a position as shown in figure 2
from figure 2 we see :2AC=AP=HQ< HG+GM+MN+NQ=EF+FG+GH+HE
figure 3 shows the equivalence will be taken when E,F,G,H are midpoints of AB,BC,CD,and DA respectively
2AC=AC+BD=EF+FG+GH+HE
rectangle.jpg