[toán 8] hình

S

schoolsmart

D

demon311

ĐỘI 5

Untitled_zps54dfbed6.png


Kẻ $BH,DI \perp AC \; ; \; (H,I \in AC)$

Ta có:

$\dfrac{ S_{\triangle AOB}}{S_{\triangle BOC}}=\dfrac{ S_{\triangle AOD}}{S_{\triangle COD}}=\dfrac{ OB}{OD} \\
\rightarrow 4S_{\triangle AOD}.S_{\triangle BOC}=4a^2.b^2 \\
\rightarrow S_{\triangle AOD}+S_{\triangle BOC} \ge a^2+b^2 \\
\rightarrow S_{ABCD} \ge 2(a^2+b^2) \ge 4(a+b)^2 \\
Min \; S_{ABCD}=4(a+b)^2 \leftrightarrow a=b \\
\rightarrow AD // BC
$
 
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