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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

- Thread starter Albert
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- Thread starter
- #1

- Jan 25, 2013

- 1,225

- Thread starter
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- Jan 25, 2013

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construct OM $\perp CD$

point M is the midpoint of CD

$PC\times QE \leq \dfrac {PC^2+QE^2}{2}----(1)$

$PD\times QF \leq \dfrac {PD^2+QF^2}{2}----(2)$

BUT $PC^2+PD^2$=$(CM-PM)^2+(DM+PM)^2=2(CM^2+PM^2)$

=$2(CM^2+OM^2)=2OC^2=8$

also $QE^2+QF^2=8$

$\therefore (1)+(2)\leq \dfrac {(8+8)}{2}=8$

and the proof is finished

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