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- #1

#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

DA respectively , please prove :

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

and determine when the equivalence can be taken ?

- Thread starter Albert
- Start date

- Thread starter
- #1

- Jan 25, 2013

- 1,225

DA respectively , please prove :

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

and determine when the equivalence can be taken ?

- Thread starter
- #2

- Jan 25, 2013

- 1,225

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